I am currently in the delayed entry program and my squad is leaderless. What should I do to show that I deserve squad leader and the guidon?

It's the DEP, it means literally nothing after you ship off. It will not grant you some special honorary status or leadership position when you arrive to Boot Camp, you'll have to earn your position at that time.

Spend your time getting your life in order before you leave. If you have that down, spend your time working out. The military is a great introduction to a lifelong engagement with fitness

They must have changed things since I was in DEP - I don't remember being in a squad or any of that. In fact, I'm pretty sure I missed half the DEP functions because I usually had to work. I was in DEP in college in some program they had (not sure if they still do) called College First. You had 1-2 years of college left, signed up in DEP and you go after college, you get college loan repayment. That's the only reason I joined. But I don't remember squads or any of that but a lot has changed. I thought they called it something else now - wasn't it called Warrior something program instead of delayed entry? Idk.

What makes you think you "deserve" to be a squad leader?

How is your Squad Leaderless? Why do you feel that you deserve a shot at the Squad Leader slot? I applaud your enthusiasm, but as of right now, you do not have the experience to be put in charge of anything as big as a Squad and lead it effectively. To be an effective Leader, first you must be an effective Soldier. That comes with experience. But, you can volunteer to take on tasks that need to get done. Start small. Talk with your Platoon Leadership to see how you can take charge of things to show you can do what needs to be done.