Can you Step up voltage with LDO
No, a Low Drop Out Linear Regulator cannot be used to boost a voltage up. That specific one has a Drop out of 0.1 ~ 0.25 Volts, so the maximum V OUT is VIN - 0.25 Volts.

You need a Boost circuit. Depending on your specific current needs, there are different types of boost regulators that will work. A charge pump uses a few capacitors and will be the simplest for under 200 mA. Otherwise there are plenty of normal regulators that use an inductor and diode pair, with internal mosfet, that can be used.

TI and every other manufacturer have tools that basically design it for you.

The three other options, since you have a 5V power source in the first place, are:


Parallel the 5V to 3.3V PMIC with a 5V to 3.8V~4.0V LDO. Less complex, and no need to double up on 5V down to 3.3V, then up to 3.8V.
Change the PMIC to be 3.8V output, and use an LDO to get 3.3V from that.
See if you can just change everything to 3.6~3.8V. No more multiple regulators.