First is first,
If you don't have any, make a datasheet.
At the first step, I highly recommend making some measurements (best with a current limited bench power supply), to find out the exact characteristics of the led blacklight. By the Aliexpress link, it seems to be (presumably true), it works out with three white LEDs, all connected parallel. In this configuration, I suggest using an
8-10 mA current limit and a
maximum voltage of 3.3 volts. Check the backlight (if there is nothing, it's also a good idea to make a simple code to make a full white screen (or use a screen testing firmware). Current limit may be
up to 30 mA as an absolute maximum value. But do NOT go over this! Theoretically, near the Vf value, there is no resistor needed in series, but, due to manufacturing variance, it may be a good idea to have one in the final design (10 R may be fairly enough). For most white LEDs, Vf is around 3.1 V.
With measurements, you must fund out:
- the minimum voltage where the LEDs lite up,
- the optimal voltage where you find the LEDs bright enough for your needs,
- the current in mA, where you find the LEDs bright enough for your needs.
These three numbers are all mandatory to follow in your design. I'm afraid, as many others mentioned before,
this configuration is not capable to produce the minimum voltage value (Vf or forward voltage) to light up the LEDs.
Based on these numbers, and the capabilities of your logic (MCU), there are many solutions. But without the actual data, it's just a trial-and-error game (with a risk of burning your MCU) to go anywhere forward.
Of course, there are many more steps after the measurements.