Wakuptime from deepsleep

I’m planning to build a small remote control on batteries. I put it to sleep with deepsleep and wake it up with a low signal on rst pin. Woks jut fine, but it takes a while to get the esp online.
So it seems not the ideal solution for a remote. Estimate the time to boot and online to about 10s. Is there any way to speed this up? Is the only way to wake the esp with the rst pin? It would be nice if I just could wake it up and resume.

Assign a manual IP if you have not done so already and use the following wifi option:

fast_connect: true

I have manual (static) ip.
Manage to speed up the connection time from ~8s to ~4s with the fast_connect flag.
Is this there any other way?

Have you tried specifying a channel and bssid (mac address of the access point)?

4 seconds is pretty fast to connect after deep sleep from my experience
if you need be faster (instantaneous) then you need to be always connected (not good for battery operation), usually this is used to transmit sensor data where timing is not priority one, but battery life is