Okay... In spite of what was stated, a Pi3B+ with nothing but a basic keyboard, mouse, and monitor connected should run on 2A. Of the specification of 2.5A, 1.2A goes to USB devices. The HDMI port is limited to about 50mA, so that doesn't tell you anything.
Now that said, a 2.1A charger may not actually deliver 2A at 5v. As the load ramps up, the voltage is likely to drop below what the Pi requires. Plus, the USB cable connecting the charger to the Pi may have very thin wires that won't allow enough current to flow without dropping the voltage to below and acceptable level. However, given that you don't report a "lightning bolt" icon on the screen, it's likely that the voltage is holding up okay.
Rather more fundamental here is that NOOBS is not actually an OS. It is a limited installer program. I wouldn't want to count on it to be able to find anything connected wirelessly, especially through BT.
Advice...especially now that you have an RPF PSU (so low voltage and inadequate current isn't going to an issue), connect a wired keyboard and wired mouse and try again. Alternatively, install the OS you want to use (I'd suggest Raspbian) directly on the SD card.