Just apply for the sales tax permit, do not mention previous sales when you do so, but do say the start date for the business is before the first sale date. (by the way, LLC is not a business type and really has nothing to do with anything in terms of accounting or taxes)
Then file your sales tax report when required.
I question the validity of a resellers permit though, you are renting, ergo they are not buying for resale - which is what that form is all about. I would ask to speak to an auditor ( I always talk to auditors, but that is me) or other customer service rep (write their name down, date and time) and explain that you will be renting, and if a company you rent to should give you a reseller pemit is it ok to not charge sales tax on the rental.
The onus to abide by the sales tax requirements of when to tax or not, is on you not the renter/purchaser. Or rent sales tax included and pull it out to report it, allowing the renter to think he is getting over if in fact he is not using that permit correctly.