I've played a few public games before. Realistically if you don't join in the first two hours of a run the base will already be so large with so many different expansion operations going on that it's hard to keep up or have fun. Especially because so many people have megabase blueprints they just keep rubber stamping down.

Its more fun to have a close group you play with regularly and can schedule online times with.

There are a lot of ways to jump into a group and have fun. You can find someone who knows what their doing and ask them to teach you. Depending on the game there are tedious steps in the process of doing basically anything, you can learn those steps and do it for them, like hauling resources or organizing items. You can find a niece to fill. Like for me, I love fishing minigames. A lot of people find it boring. So when I start a new game I usually fish if it's available. That way I contribute food and whatever else you can fish up.

Edit: I didn't see that this was Factorio specifically, but in general I think the advice stands.

Look at the production and consumption stats and find where the factory lacks is where I'd start. Never did multiplayer with randos though

I remember there was a multiplayer server in this community about a year ago. I never joined and I don't know if it's still there:

https://hackertalks.com/post/4740904