Theoretically TP4056 is capable of charging at 1.4A. Practically your design is limited to the capability of the USB source par the picture or your external source. You need to change the resistor on Program pin on the TP4056 to the desired charge current
Per the circuit above the resistor is R4.
Also from the LTC4056 data sheet:
PROG (Pin 5): Charge Current Programming Pin. Provides
a virtual reference voltage of 1V for an external
resistor (RPROG) connected between this pin and ground
to program the battery charge current. In constant current
mode the typical charge current is 915 times the current
through this resistor (ICHG = 915V/RPROG). Current is
limited to approximately 1.4mA (ICHG of approximately
Based on the maximum available Li-Ion battery capacity you should be able fully charge the battery under 4hrs.
Word of caution: Although you might want to charge at 2A the battery chemistry might not recommend such a high charge rate. Read the battery chemistry specification very carefully. Improper use can be dangerous. For example LG Chem 18650 MH1 has a standard charge current of 1.5A and Max charge current of 3.1A.
Below is a chart on charging Li-Ion batteries. In most cases it is recommend that the battery be charged 0.8C. Also as the battery reaches full capacity the charge rate also drops as described by the chart below
The advised charge rate of an Energy Cell is between 0.5C and 1C; the complete charge time is about 2–3 hours. Manufacturers of these cells recommend charging at 0.8C or less to prolong battery life. Most Power Cells can take a higher charger. Charge efficiency is about 99 percent and the cell remains cool during charge.