I have attached a few oscilloscope captures here.
First, the basic board powerup. Yellow is the input voltage from a DC adapter to the board. Blue is the 3.3V supply connected to VDD_HIGH_IN and VDD_SNVS_IN. Purple is 1.35V for VDD_SOC_IN. Green, shown one division higher, is the voltage at USB_OTG1_VBUS, the same port where USB is connected to my computer. You can see that USB_OTG1_VBUS is solid at a touch over 5V the entire time of powerup.

Then I have a capture that shows the POR_B signal (green) which is driven by a Texas Instruments TPS3825-33 reset supervisor. The time between VDD_SOC_IN rising and POR_B going high is 172ms.

There is a brief time that POR_B (green) is rising with the 3.3V supply, but it goes low once the reset supervisor has enough voltage to operate. That is shown here, zoomed in from the previous capture.

With regards to BOOT_MODE[1:0] that should permit getting into serial download mode...
I have probed BOOT_MODE0 (green) and found it to be greater than 3V as long as the 3.3V rail is powered up. Sometime right after 3.3V reaches its maximum, something is applying a weak pull-down to BOOT_MODE0 that can't override the 10K pullup to 3.3V that my board has. 3.0V should be well above the VIH (0.7 * OVDD) for IO.

BOOT_MODE1 (green) is more straightforward - I have that stuck at GND directly through a switch. It stays at 0V:

We have recently obtained AN12853 "i.MX ROMs Log Events" from our distributor FAE and are working through it to see if that provides some insights on why we can't get to serial download mode.
-Michael