Hi Jorge
Thank you very much for the attached latest revision of SDP and sorry for following up late.
I've measured VCOREDIG and VCORE, both of them exhibit severe drop. But I've not measured VCOREFEF and haven't tried out the capacitor changes. However, I've some new findings so far.
Finding#1: If charger (MAX8903) is bypassed by connecting battery to SYS_4V2 domain, the board can boot up consistently. Tested over 4 boards and 2 batteries across different battery levels.
Finding#2: After adding 2.2mF cap to SYS_4V2 domain (original circuitry, charger is in-between battery and SYS_4V2), the board can boot up consistently. So far I've only tested on one board.
To answer some of your questions:
What's the current being drawn out of the battery when the voltage drops occur?
Current spike is exceeding large, see below:

Another possible issue is the battery itself. Could you please try replacing the battery with a DC voltage source with the same capabilities of the battery?
Tried simulating battery using DC (DC connected to charger BAT pins), board can only boot up when DC is equal to or greater than 4.1V.
If 4.2V DC is fed into SYS_4V2 domain and battery is removed, board can always boot up.
If 5V DC is fed into DC jack and battery is removed, board can always boot up.
Thanks & regards,
Jihua.