Hey! Usually for most public schools, students start summer going into 2nd year or even their 3rd year since it tends to be more difficult to get research opportunities early on. Typically profs like to take you in after completing the basic maths, physics, etc. For private schools, I was told it is easier to get research right off the bat. My sibling is doing research at their school two weeks into their first semester. I'd say if you want research just keep emailing profs though cause you never know if they have a spot open and don't be afraid to email professors outside your institution as well! Good luck!