The minimum number of founding couples needed to avoid close-relative marriages over many generations, the answer is far more than a handful if you wanna avoid fuckin your cousin: Here's a rough guide...

1 couple: Their children would have no one to marry except siblings, so inbreeding begins immediately.

2–5 unrelated couples: This avoids sibling marriages at first, but within a few generations nearly everyone is closely related.

10–20 unrelated couples: Better, but genetic diversity is still low, and cousin marriages become difficult to avoid over time.

50–100 unrelated couples (100–200 people): This is often considered around the lower end for maintaining genetic health for several generations if there's careful mate selection and no new people arrive.

Several hundred unrelated founders: This provides much greater long-term genetic diversity and is closer to what's needed for a self-sustaining, isolated population without frequent close-relative marriages.

So if you want to run off and start your own little community it won't be long before your children are off into the busses humping their cousins...