How to implement this function in transistor level?
The simplest transistor-based circuit is the RTL flip-flop:







simulate this circuit &ndash; Schematic created using CircuitLab

C1 is added so that the circuit prefers to power up with the output low, with Q1 not conducting and Q2 conducting. It also sets a minimum pulse width on the input signal. Once that threshold is exceeded, Q1 switches on, Q2 switches off, and the output goes high.

If you want a manual reset (other than power-cycling the circuit), connect a switch between Vout and ground.