Man, that’s a tough call. I think it depends on how you plan to use the home, as well as what you’d like to do with the home overall (simply use it as a place to live? Or offset some housing costs by renting out at least part of it? Do you plan to sell for profit any time soon (5-10 years) or are you hoping for a forever home for the family?).
While prices in Austin aren’t as high, I also live in a hot market and I have thus far refused to pay too much above asking. However, I’m a) single and b) using real estate as a separate source of income: Tenants in my first property, and now roommates in my second (current) home.
If you’re willing to dabble in landlord life (or if you’re also budgeting to care for parents/in-laws someday), perhaps one way to justify paying over asking is if you can find a home that has a detached mother-in-law plan or wing of the house, or find a property that already has an accessory dwelling unit (second smaller home, garage apartment, etc.) on site.
While these properties are few and far between, you might be able to budget for a conversion of your own with the right layout. If you’re a hard time finding an affordable housing situation within your budget, many other people are likely struggling far more and would be happy to pay rent to you for a 1/1 with a kitchenette (or even without one).
Alternatively, being open to renting a nice home or apartment with that cash for a year or two gives you a) the opportunity to really hone in on neighborhoods you know you favor for a home purchase, and b) takes the urgency out of such a huge financial decision. You could even try finding a really good realtor you trust to act on your behalf, then temporarily moving to a more affordable locale (like Texas, haha) while they play the market for you.
Of course, the gamble of waiting to buy is a) you’re not sure what your income situation will look like by the time you’re ready, and b) mortgage rates may go back up.
There are a few different ways to hack this — but mostly, my general advice is to focus on the big money (saving on the house purchase price, etc.) and try to ignore how much “small or medium” money you’re spending (i.e. a year’s worth of rent, potential renovations, etc.) if you’re still coming out ahead overall. I know that housing urgency can really trigger that kneejerk reaction of just getting it over with.
Regardless, good luck! It’s hard to adult these days. 
