Asking for job referrals

So I’m in my senior year of college applying to a bunch of analyst programs for after I graduate. I have been networking a good amount, just reaching out to people who work in my preferred industry and ask them how they got there, any tips, and what they do on a day to day basis as I just want to get as much advice and knowledge as possible.

I know it’s good to get referrals when applying to places, but I don’t personally know anyone who I can ask for a referral to.

I know some people will randomly reach out to people on LinkedIn who work in the company they are applying to and ask for a referral, but isn’t that weird? Asking for a referral to someone who u don’t even know and who doesn’t know you?

My question is, is it weird for me to ask for a referral to someone I have already talked to on the phone/had a ‘coffee chat’ with? I don’t want to it to seem like I am only talking to them to get a referral because that’s not the case, but idk how to even go about asking them for a referral.

Any advice would be appreciated, thanks.