More advice on landing internships?

Hey guys! I actually posted a few days earlier so ill keep the introduction short. I'm a freshman going to a non/semi target school and residing in NY. I am really interested in finance and am hoping to get into IB one day. A lot of very helpful people said on my previous post that a PWM internship should be fine as a freshman during the summer time. I think it would be an interesting opportunity and I would like to get the experience.

I wanted to get started on this as soon as possible so I emailed one local PWM office from several banks, such as UBS, JPM, ML, and MS. I emailed them early this week, around Monday/Tuesday. In my email, I introduced myself, expressed my interest in finance, asked for potential internship opportunities, and said I was able to provide a resume if necessary. I haven't received a response yet so I'm starting to worry.

I just have a few questions for those more experienced with the subject. How long do firms usually take to respond/When is it a good time to believe that they have no interest? Am I going about networking/emailing the wrong way? What course of action should I take if this fails/What other opportunities should I look for during the summer?

Thank you guys so much for your help and I really appreciate the community here!