At my last job we built an entire API on top of serverless. One of the things we had to figure out was this cold start time. If a user were to hit an endpoint for the first time, it would take 2x as long as it normally would at first. To combat this we wrote a "runWarm" function that kept the API alive at all times. Sure kind of defeats the purpose of serverless but hey, enterprise software.
I could imagine these to perform better.
If you aren't married to AWS, then Cloudflare Workers could also be worth a shot.