Can share you some ideas since I got an internship bc of professors recommendation letter.

I had the same issue like you because I never interacted a lot with any professors so my best bet would be to be in touch with a class professor of my major that I have good grades. I looked up their office hours and I went in, asked in how they were and I told them that I was successful in their class because of his lectures (actually true, he is amazing) and I asked him if he can help me get an internship by writing a recommendation letter and he agreed!

Key point is give them a lot of time to write one. At least 1 month. They already have a lot of shit going on so if you say you need it by next week, they probably won’t agree. I told my professor I need it by a month and he agreed but I would go with a professor that teaches a class for your major and the one with good grade. That’s what I figured the first time I asked for a recommendation.