Can I withdraw the minimum account fees for Vanguard?

To answer your question, yes, you CAN use $3,000 to open a Vanguard fund, and then subsequently remove the money; they WILL let you keep a fund open as long as the balance is over $1,000. Under $1,000, and they may decide to liquidate your account and mail you a check.

Any Vanguard mutual fund with a balance less than $10,000 is subject to a $20 annual account service fee (basically a low-balance fee) above and beyond the expense ratio. So it doesn't matter if you have $3,000 in the fund or $1,000 in the fund, you're still going to get hit with the fee. Brokerage accounts (which you would need for ETFs, but not for mutual funds) are also subject to the $20 annual fee until you hit Voyager status, which is $50,000 in total Vanguard assets across all of your funds and accounts.

You should not be "investing" with money that you may need in the short term. Don't invest until you have an emergency fund. What happens if you put $3k in, buy some stocks, bonds, or mutual funds and then the market drops in the short term, you're going to take a loss when pulling the money out suddenly.

Why?

The Vanguard Fund you specifically mention is a RETIREMENT Fund....why would you be putting even a penny in there if there was a probability you were going to take it out before age 59.5? You would DESTROY all the benefits offered you for retirement AND pay a hefty penalty for doing so!

Put the money in a Savings Account (or a shoebox under your bed!) if you are going to "need" it! Silly goose!

If you might need to take part of your retirement money for something you want now, you are not ready to save for retirement (and will probably be poor when you do retire).