Not an option for spouse of GC holder. Your fiancee cannot adjust status while in the US on VWP/ESTA, even if you get married today.
From https://www.uscis.gov/policy-manual/volume-7-part-b-chapter-7 -- "A noncitizen admitted as a nonimmigrant without a visa under a Visa Waiver Program is barred from adjustment of status.[...] These bars do not apply, however, to those seeking to adjust status as an immediate relative of a U.S. citizen or VAWA-based applicants."
Regardless, if you are ready to get married now, go ahead and do so while your fiancee is in the US. You may file an I-130 for her after you have a valid marriage certificate. Then she should leave before her 90 days on ESTA are up. She may visit the US again, even while the I-130/F2A case is pending, subject to CBP inspection as usual.
Also, I recommend you apply for naturalization soon after you are eligible. Once you become a US citizen, you may request for your spouse's visa case to be upgraded to IR1 (spouse of USC). That way, the visa bulletin will be irrelevant to her case, and she can be in line for visa interview soon after I-130 approval and NVC review. At least, much sooner than if her case remains under F2A (spouse of LPR).