Picking a voltage regulator for 12V/10A input -> 3V/290mA output
No, that  MIC5219-3.3YM5-TR will not cut it, you need something beefier than that.

But first: this is how adapters work, a 12V/10A adapter supplies 12 V with a current between 0 (zero) and 10 A.

The adapter does not supply the 10 A, it can supply upto 10A. How much current flows depends on the load, so not the adapter. As long as the load does not require more than 10 A, this will work with the 12V/10A adapter.

A regulator (like the  MIC5219-3.3YM5-TR) is simply a device that takes an input voltage, 12 V for example, and converts it to a lower value, like 3V. The 9 V difference between input (12 V) and output (3 V) has to "go somewhere". The simplest is to converted to heat but more heat is generated as the current gets higher, uint128_t's answer shows that in your case (0.3 A) quite some heat is generated. So the regulator will need cooling in the form of a heatsink. You need to do some calculations to determine what heatsink you need.

But the MIC5219-3.3YM5-TR cannot even handle the amount of power (resulting in heat) that it would need to dissipate for your 300 mA so we need to look elsewhere. There are other linear regulators that could do the job like the old LM317 but this is old hat and inefficient and still requires a large heatsink.

Fortunately there's a simpler and cheaper solution that does not require a  heatsink. This uses a switching regulator. I recommend an L2596 based module which you can buy on for example on ebay. They're cheap, you feed it with the 12 V from your adapter, then measure the output voltage and use the potmeter on the module to set the voltage to 3 V. Yes it is really that simple. I often use these modules and they just work.