It's doable but you'll need a cement mixer.
Not for the volume, but to get an uniform mix.
First you need a water barrier, injection is the most common here.
The most time consuming will be making a barrier around the problem area with temporary ply.
Then fill with a very liquid self levelling concrete; pour a little, spread, pour a little, spread, etc, until you have filled to your mark.
With what I've used, I expect at least 24 hours before removing the barrier and 3 to 5 days till you can do any work on it.
In Belgium, we have additives such as "Conpaktuna" that make the concrete flow better and water proof, you need to check what is available locally.
http://www.compaktuna.be/en/compaktuna-10.htmI don't get why you need a subfloor for about 3.8cm, pictures would help!