When there are multiple bids on a property, or it is being sold as distressed (i.e. short sale, reo, etc.), a good way to help get your offer accepted is to keep things super clean by not asking for a termite report or work to be paid by the seller.
As a Buyer in CA, you have pretty much unlimited access to inspect the property for whatever reason, up until closing. You can get your deposit back, no questions asked, up until you remove contingencies. After contingency removal, you can still back out, though some or all of your deposit will likely be put at risk. Anyway, for $85 you can have a licensed termite specialist inspect the home and draft an official report.
If there is a standard amount of work to be done, say less than $2,000, then having you eat this expense is pretty much what you signed up for, though everything is negotiable if you are prepared to walk from the deal.
If the expense is greater than $2k, or more than you were prepared to spend, then you have the option of pushing back on the seller, saying this expense was not baked into your offer, and request them to pay for it. With agreement from all parties, you can always amend the purchase agreement after escrow started.
One reason to keep the inspections "out of the offer"... meaning, not requesting it up front in the purchase agreement... is that your lender will absolutely require the work to be done before closing, regardless of who is paying for it. This can present somewhat of a challenge if you are going to pay for work on a property you don't yet own.
Meantime, since your home is only 7 years new... it would be surprising if it sustained significant termite damage, but it is always good to know up front. $85 is a small price to pay for peace of mind.
Congrats on the purchase.