the honest answer is: sometimes. here's the framework i actually used to figure out whether it was possible in my situation.
first, diagnose the source. burnout comes from different places and not all of them require you to leave.
workload burnout: too much, for too long. this can sometimes be fixed without leaving if you have a manager willing to renegotiate scope. the catch is that most workload burnout happens because the manager is either unresponsive or the problem. so the fix requires having the right manager.
values burnout: the work feels meaningless or actively wrong. this one is harder to fix without leaving. i've watched people try to rediscover meaning in roles that had drained them of it. it rarely works. the brain has learned that this work = meaningless. cognitive retraining is slow.
relationship burnout: the problem is one person or team. this is the most solvable without leaving, if you have organizational mobility. a team transfer, a new manager, even a cross-functional project that physically removes you from the dynamic can help.
identity burnout: you've been this job for so long you've forgotten who you are without it. this one doesn't require leaving but it does require building an identity that isn't dependent on performance. therapy is more useful than a job change here.
i had workload + values burnout as a senior ML engineer. i tried the manager conversation. he was sympathetic and genuinely tried to reduce my scope. the values piece didn't change because the product didn't change. i was building recommendation systems for engagement metrics i'd decided were harmful. less of it was still it.
i left. i took a research role with a university collaboration. compensation took a hit, intellectual interest went up. the burnout cleared in about four months.
if you're trying to figure out whether to stay and fix it or go: be honest about which type you have. the workload one is recoverable in place. the values one usually isn't.