How about you actually work harder for it, go the extra mile and do stuff that others don't do to make you shine and show the lead team you're capable of joining them.
Ways of doing that is being more active, helping anyone with anything whenever possible, training and helping new staff, helping LT members will things such as reports and application strawpolls and showing leadership. There is a lot more that you can do but those are just some of the things.
You may think that you do some of those already but the reality may be that you don't. That's what I thought of myself but then many people including LT members themselves helped me and that helped me to improve even further.
If you need help, just ask me, a lead team member or ex-LT member.