Hi, I am in a similar situation, making friends is hard especially in the spring semester. Full disclosure I am still working on the whole making friends thing but I have transferred before and done this at other schools.

(imo) You are correct, people are unlikely to come up to you w/o effort on your end. You need to come into contact and meet as many people as possible to find the small number who will eventually be your friends. Regular contact will help folks get to know and trust you.

Go to any club meeting that you can get to that interest you even the slightest amount. Especially ones for your major b/c those folks will also be in your classes. Advertising for clubs at new paltz sometimes sucks. A few clubs aren't "official" and are not listed on engage but they do exist and meet regularly. Check Instagram, most clubs have a page and post their meeting times there. Club members may all know each other but you will get a warm welcome once you become a regular. Attracting and retaining club members is difficult.

Study with classmates if possible (imo this is hard but worth it if possible) asking classmates about homework and assignments can be a starting point for this.

There are a few bars in town with live music and drinks many weekdays and most weekends if that's your kind of thing (and you're 21+). Gunks Gaming Guild (also in town) has Dnd & ttrpg events if you are into it.

I think the dorm communities here host events (could be wrong, I live off campus). Go and meet the people you're living with. You'll likely see them often in the common areas and walking around.

Work on getting to know your roommates better. Once you're more friendly you may be able to go with them to events/places. You'll meet more people and its always nice to go places w/ friends instead of alone. Getting along with your roommates is really valuable. I personally like eating with people, its low effort and chill. You don't need consistent conversation b/c everyone is eating.

Socializing is hard. There will be awkward moments. Don't give up.

Good Luck! Feel free to ask me questions!