I have promoted a fair number of account managers into senior and team lead roles over the years, and the pattern is consistent enough that it stopped surprising me. The people who got tapped were rarely the single best performer on the scorecard. They were the ones other people already treated as a resource before the title existed.
Become the answer to "who should I ask"
When a newer AM gets stuck on a tricky renewal or an escalation they have not seen before, notice who they go find. That person, informally, is already doing part of the job a team lead does. If you want to be that person, make yourself easy to ask: answer questions without making people feel behind for asking, and follow up to make sure the advice actually worked.
Document what you know before anyone asks you to
Most account managers keep their best scripts and workarounds in their own head, because writing them down feels like extra work with no immediate payoff. The ones who get promoted tend to do it anyway, in a shared doc or a wiki page nobody assigned them to write. When a manager is deciding who can scale their knowledge across a team, the person who already wrote it down is the obvious answer.
Take ownership of the problem nobody assigned
Every team has a recurring issue that falls into the gap between roles: an onboarding step nobody owns, a handoff that keeps dropping information. Fixing your own accounts is the job. Fixing the gap that affects everyone else's accounts too is what gets noticed above your manager's head.
None of this shows up on a quarterly scorecard, and that is exactly the point. A scorecard measures whether you can do the job you already have. The move to senior or team lead is a bet on whether you can do more than that, and the only evidence available for that bet is what you did before anyone asked you to.