> I wanted to know if it would be smart to withdraw the funds from my 401(k) to put towards my emergency fund and speed that process up

Unless you like lighting money on fire (~$160 for you), this is always going to be the wrong answer.

> or if I should treat the account like it doesn't exist until I reach a point where I can safely contribute to the account again.

Keep it invested in the 401k.

Or roll it over to new employer 401k.

Or roll it over to an IRA at a brokerage of your choice (ie Fidelity/Vanguard/Schwab).

Keep it within the confines of a Tax Advantaged Account (ie 401k/IRA).

Keep it invested.