Solved. Using a 0.5mm wire, I could successfully boot.
Now waiting some components to build my own dock, with USB functionality as well.

Thanks for the help.
I bought the tantalum capacitors (22uF, 0,47uF).. I'll try with them.
Also bought 20 awg (0,5 mm) wires.
They may arrive on tuesday. I'll let you guys know of my results.

Thanks all of you for the comments. They're being really helpful.

@Chris Stratton,
I added 2 caps (220uF in and 470uF out), to try and get that bigger transient response. Tried with a Turbo power charger (max 3A, as Omega would not request that).
But also didn't work.

Now, I noticed something strange. My regulator outputs 3.3V, but as soon as I connect my Omega to it, output instantaneously drops to around 2.9V. I have no idea why it being in parallel, would cause this drop.

Any suggestions now?

Does anyone know which Capacitor values are used in the original dock?

I tried using only the AMS1117 without caps, and it had the same behavior.

I could connect my Omega2+ to my PC using a FTDI and got the logs.
It always ends like the following:

[ 18.515046] EEPROM:Read from [factory] offset 0x0,length 0x400.

I'm going to try using capacitors both in and out.

I received my Omega 2+ but I didn't buy a dock (thought it wouldn't be needed).
So, to boot, I first tried using Arduino to provide 3.3V but I noticed it doesn't provide enough current.

I then bought a YwRobot (protoboard power supply) that has an AMS1117 3.3 voltage regulator that can provide up to 1A output.

My Omega2+ then starts, LED turns on and stay on for about 20~22 seconds. It then turns OFF and nothing else happens.

So, I decided to use a Lab Power Supply, and the face the same behavior. It turns On for about 20secs and turns off. I was able to see that while the LED is on, Omega is consuming around 180 mA, and when the Led goes off, it keeps consuming around 60mA.

The link to boot without a dock, tell to use LD1117, but uses no Capacitors around it. while the YwRobot has cap.

Any other suggestions on how to boot it without a dock?
Might I replace the LD1117 (I'm not finding it around), by a AMS1117? Should I skip the capacitors recommended by the regulator manufacturer?

Thanks