What is an airliner pilot's first go-to if he or she doesn’t have a positive climb rate immediately after take off?
The first thing I would do is advance thrust to maximum available thrust, make sure both engines are indeed operating.
Next I'd check is if the speedbrake is stowed.

I would not consider retracting flaps because when you are too slow to climb you are definitely too slow to retract flaps... could be deadly.

Normally this kind of situation can't happen unless you have at least one engine failure and the remaining engine not working at full thrust or the wings are contaminated with ice or snow. The aircraft is perfectly capable of climbing on one engine, so if you have two engines on max takeoff power and are still not climbing then something is seriously wrong.
In case of ice/snow on the wings, well there is not much you can do about that in the air, put on wing anti ice and hope that it is quick enough to clear the wings of any contamination, this comes at a penalty of losing precious thrust because of the bleed air extraction. This situation is usually avoided by removing snow and ice from the wings whilst still on the ground - before taking off.