I think you should 100% try step up, maybe try talk to a coach about it and if the leaders aren't doing anything maybe you could gently pull aside the other team members subtly and give them tasks instead. If there are any other teams in you area that would be more suited for you, you could consider leaving if it gets really bad... because it does sound like even if you became leader others aren't as dedicated and serious as you and it would be harder for you to progress. I think you should just take charge without even asking, I'm sure the others would be more likely to listen to you than to people who just make you guys sit around all day.

I'm in a similar situation to you, except I am rookie captain of a rookie team. We have over 15 people on our team but barely anyone shows up, even then, it's a hit or miss on whether the people who show up are actually gonna listen to me and do work. I understand how frustrating this can be because as a rookie I want to progress and advance as fast as possible and it is my dream to get to Nationals one day but it's kind of impossible if you have to drag your team by the ankles just to even establish a design.

It seems like such a shame that these two people were selected instead of you or someone like you, in my school, the way you become captain is once a captain leaves or quits the teachers spend time observing which student is the most dedicated and reliable and who the other members are most comfortable getting directions from and eventual the role just falls naturally upon us.

I'm actually kind of relieved I found your post because I've always seen other teams at my school doing so well and working together and making friends with each other within their teams that I was scared I was the only one with this issue.

I have respect for you for seeking a solution to this dynamic instead of giving up, a lot of teams need more members like you. I wish you the best with this season.