You just described closed-loop control system oscillation. Cause is wrong gain and/or delay parameters. AWS ASG has some knobs for tuning like Cooldown, MaxSize. What you described above is most probably long boot time (delay) problem. Service should be ready in less than 30 secs after boot. To get there, one should bake AMIs, not install afresh all the stuff on boot.
Lazy loading of modules is a common cause, but any other resources that are loaded on demand or in the background. But that's more of a situation of thinking you need two additional nodes, getting three, settling back to two after warmup, and then killing them all off again when the spike ends.
I may have said elsewhere that I'm more comfortable with scaling load based on daily and weekly cycle patterns, with perhaps a few exceptions for special events (sales, new initiatives, article publications) and making it easy for someone to dial up or down.
To use a car analogy, get really good at power steering and power brakes before you attempt cruise control, get really good at cruise control before you attempt adaptive cruise control. And don't even talk about self-driving unless you're FAANG.