Green’s Dictionary of Slang

jump off v.

1. [mid-19C+] to begin, e.g. of a military attack.

2. [late 19C] (US) to leave.

3. [1930s+] to happen, to start happening.

4. [1970s] of a person, to start doing something.

In phrases

jump off the porch (v.)

[2010s] (US black) to start a career selling drugs.