I know for example in Japanese, instead of saying 私はライアンです (I'm Ryan) it becomes ライアンです "(I'm) Ryan" as that sounds natural, it's like if saying "I've traveling to the US." which simply in Japanese becomes イギリスに旅行に来ました. Basically it's rewritten as "(I'm) traveling to the UK". (This nuance often gets mistranslated via anime or JP media).
In this case by saying アメリカに旅行に来ました [There's no 私は in this sentence] is akin to saying "Traveling to the US" when omitting I'm entirely, so you have to infer "who" which in this case is the PERSON IN FRONT OF YOU or TEXTING OR CALLING, so you've established who you are talking to based on presence of mind and situational awareness.
You need to use own brain to infer based on context rather than being direct (as in Japanese), if the speaker says "Who are you talking about" when omitting "I'm" or "We" or any other proverb entirely, you refer to yourself by stating amongst the lines of "You're talking to me, right?" to convey to the speaker that you're are the person they are referring to.
For example, if saying お腹が痛い "~~(My)~~ stomach hurts" [It's not: 私はお腹が痛い] as YOU or the [PERSON] in question is the subject, so there is no need for 私は (I am / my) but if they said 誰？(Who?) then simply state 私です (Me.) to clarify afterward. But saying 私 alone sounds robotic, that's how they would know you're using Google Translate.
Try reading this sentence (with subject omission akin to Japanese - absence of pronouns such as I'm, we, us, we're, and so on, The result below is what it would like if it was written in the Japanese format:
財布をカバンから出し、好すきな子の為に高い宝石の支払いをした。
Took wallet out of bag and paid for expensive jewelry for the girl whom liked.
It's definitely not written as:
彼は彼の財布を彼のカバンから出し、彼は彼の好すきな子の為に高い宝石の支払をした。
Seeing 彼 5 times in one sentence drives me insane and annoying to read, as there is no point, so in Japanese they omit it entirely, you HAVE to INFER on context. (The sentence: 財布をカバンから出だし、好すきな子の為に高い宝石の支払いをした from Japanese feels more natural to read without saying 彼 over again.)
The complete sentence (pronouns ommitted - conveyed in brackets) from Japanese:
(I) took (my) wallet out of (my) bag and paid for expensive jewelry for the girl whom (I) liked.
This is one of the reasons why a language like Japanese gets "lost" in translation, for example in manga or anime subs, as there is no 私 or 僕 in every sentence the same way as it is in "Western" languages, from their eyes it is considered "Vague" if they are not aware of Japanese grammar.
It does pose issues for inexperienced translators from JP > EN as they find it hard to distinguish on who to pinpoint since they do not use "I am" in the same way as English, since Japanese is a "pro-drop" language, in which pronouns or possessives are omitted, as they expect the audience to infer based on context.
I mean, can you still understand it if you OMIT the subject or pronoun to the same extent as Japanese, but in English sentences? Like this one:
went to Times square to meet up with a friend who lives here, such a good (pal).
Preface: I'm no linguist. Just someone who speaks both JP and EN. But boy do I love thinking about stuff like this. I'm not going to answer your original question though, cause the short answer is really just no.
Subject omission in JP is somewhat interesting because it's tied to their culture, but I'd like to sort of push back a bit on the thinking that it requires some thinking to figure out who the subject is.
Japanese is a context-heavy language, and this subject omission is an important cultural rule under that. But it does mean that the context needs to first be established between participants.
Suppose you walked up to a friend, waved at them, and said イギリスに行った (lit: went to the UK), most JP speakers would first think that you're talking about yourself. But if, prior to this conversation, say the day before, you and this friend A were talking about another friend B, and B was deciding where to go and you went to the airport with them, then this friend A would be the only one to know that you're talking about B.
But suppose it's been a few more weeks before meeting with A. Then A might think you're still talking about B, especially if you've not mentioned going overseas to A. Then a misunderstanding can happen, and the onus is on you to clarify who you're talking about in the first place. You'd be thought of as someone who can't "read the air" if you constantly leave the subject vague without considering the context you've thus far established with others.
Friend A can certainly ask for clarification if they know your tendencies, and within their own personal context. 「Bが？」 (t: B did?) they might ask. 「いや。私。」(t: No. I (did).) you might reply. Notice how I just used 私 with no particle; the particle is implied!
I find that a lot of newer learners have a tendency to really focus on this particular aspect of the language. I actually don't find it to be something that speakers need to expend on a lot of energy on. You know who you're talking to, and thus know and share enough context to carry on with the conversation. It's also common to remind each other of which context is being talked about to jog your convo partner's memory. If you have trouble remembering context, you can always play it safe and be sure to explain yourself, or check if your convo partner remembers it.
Oddly enough, I have a friend who got a bit turned off by this "feature" of Japanese and discouraged him from learning by a bit. He's always had questionable memory, so having to sort of "remember context" is a bit of a difficult ask for him. I don't think "remembering context" is a strict requirement to be a good speaker in JP cause it'd just be a quirk of his like it already is in EN. Us English speakers like to think we're quite rid of context when we compare it to the Japanese, but how much we know each other is context too.
Also, a small comment: just saying 私 in reply to your example for 誰？ isn't necessarily weird or robotic. It depends on your relationship with the speaker. If you usually use the polite form with the person, then yes, you should append with です.
Now, if you didn't have the previous part where you're talking about having a stomachache, then even to a close enough friend, it's more natural to respond to the "Who?" with 私だ - not too different from EN in this case: it's "Me" vs "It's me".
And when the sentence is お腹が痛い, you're 100% talking about yourself. If you're actually talking about someone else, it should be お腹が痛そう (looks painful) or お腹が痛いって ((person) said their stomach hurts).
One thing I commonly see in comments out of threads like this is the oversimplification of how the Japanese communicate. They might be polite and sometimes avoid mentioning the subject for convenience, but when you need tell someone to do something, you can do just that, with different levels of politeness.
The Japanese is expected to be polite to strangers. But they don't interact with people they're familiar with in the same way, as it's usually perceived as a distant way to communicate.
Edit 1: Formatting and grammar