What is the very basic electronic component to generate pulse wave (high or low) we commonly see in digital?
Usually we do not pull random 1s and 0s "out of thin air". Binary signals exist for reasons. So what kind of signal do you want to generate?

You can make a signal that is always low, or always high, just by connecting a wire to the ground rail, or the power supply rail.

You can make one that alternates between 0 and 1 by using a clock.

Any signals more complex than that are generated using logic circuits.

A computer keyboard, for example, sends 1s and 0s depending on which key you pressed. At least, an old PS/2 one does - USB is quite complicated so let's ignore it for now. The keyboard has a bunch of, guess what, switches (one for each key) and logic gates to work out the correct code to send based on the switches.

In practice, if you want to generate a signal like this, for testing purposes, if the speed (bit rate) is slow then you would use a microcontroller. For very fast signals you could use a SERDES (fed by several bits in parallel from a slower microcontroller), or an FPGA.