Need access to funds that were earned & taxed prior to establishing LLC

"To access these funds now, I believe they need to be considered distributions, and pay capital gains tax. "

This is likely not the case. When you transferred personal money to the LLC, you should have recorded it as either a loan or some form of capital increase. Taking the money out should be considered a reduction of your assets in the LLC, not a taxable distribution.

However you may want to review whatever documentation you have from that point in time to be sure that you can record everything appropriately. As an example - did you intend for it to be a loan, but never charged the LLC interest for the use of your funds? Legal advice may be required to ensure everything is above-board.

If you don't have an accountant already, I highly recommend that you get one to help you with this.

I assume you have or will elect to have your LLC taxed as an S-Corp. From your comment, it seems that your goal is to reduce self-employment tax and the only way to do that is to elect taxation as an S-corp.

Assuming this is the case, you should be able to undo the transfer of money to your company bank account as explained in the excellent answer by @Grade 'Eh' Bacon. You'll need an accountant's help to get this right.

You should also note that Trump created a 20% tax deduction for sole proprietors and LLCs with pass through taxation (i.e., not S-Corp taxation). If you elect S-Corp taxation you lose this tax deduction. There is thus less, if any, benefit to electing S-corp taxation with this Trump tax deduction. Though who knows how long the Trump tax deduction will last...