My 24th Birthday is just in 7 days and I am feeling so damn old. What should I even do?

I am 23 turning 24 on this 22nd December and its scary how I am still single at this age. Never had a gf. I am feeling as if I am running out of time. I am studying MBA and talking with multiple girls in my University who are 21-25 age range but nothing much is happening. I tried asking 3 of the girls to hang out with me a couple of weeks ago but all 3 said they had class or assignment to complete. Is it really too late? With most of the girls my conversations had been short but even with the ones with whom my conversations are good, they arent very responsive to me on social media like Instagram or doesnt really hang out with me and our conversations are limited to within the University environment. Is having 0 relationships at all at almost 24 a red flag?