For this we can access the console, for those unaware: the console is like a terminal where we can enter commands.

The console is by default enabled, and can be opened on your computer desktop by pressing "~" (tilde) while the Half Life window is active.

To skip the boot scenes, we need to enable cheats:

sv_cheats 1

Next we need to jump to the map right after the boat scene, simply enter:

map d1_eli_01

and press Enter - you'll go to Eli's lab.
You can even skip that if you like by going to the map right after that (Ravenholm!):

map d1_town_01

Same trick can be used for skipping the car driving scene's:

map d2_prison_01