What are the odds that I am dealt a big pocket (JJ or better)

As a super tight player and watching the big rake/blinds, I am wondering how long I have to wait to shove as short stack.

How many hands to I have to wait to get a pocket Jack or better?
Thank you in advance.

JJ+ is 24/1326 which is 1.81%

This is dreadful poker btw and the questions you are asking won't help you get better.

Better would be to ask... if I'm short stack, what range should I be looking to shove with?

Clue - wider than JJ+

Actually an even better question to ask would be... why am I short stack in a cash game?

I noticed that loose players will call short stack all in with ease.

Ok, so you think that playing a super tight range with a short stack is a better strategy than playing a medium range with a full stack?

Short-stacking is all about all-in math. Doing EV math for semi-bluffs to find out what hands are guaranteed to make a profit against what hands is the best place to start. Just glancing through the Spoonitnow files, this article goes in-depth on how to figure out your EV when shoving with equity and even includes how to automatize it with spreadsheets and this one applies it directly to preflop scenarios. You can skip right to "shoving over someone preflop" in the second article to get the most directly relevant material, but it can be useful to go through the first part of the article to look at how the math works for your opponents. (Eg: How wide can your range be while still putting him in spots where large swaths of his range are -EV or indifferent?)

Play with different ranges for villain. If they are opening 15% and you have AJs, is there a range they can continue with that makes a shove -EV? What about AQo versus a 10% range?

A ton of postflop scenarios boil down to these same shove or [x] decisions too, so it's practically your one-stop shop on how to play short-stack poker.