RSU's absolutely do count for income for mortgage purposes. (Source: I've bought a house recently and my RSU's were accepted as part of my income). It's different if you work at a startup, where the stocks are not yet publicly traded, but if you are working at FAANG it is publicly traded, then the stock is quite liquid, so banks consider those RSU's to be as good as dollars.
You just need a document from your employer demonstrating to the bank what they are intending to pay you per year in total compensation, including both salary and RSU stock. Also get some documents from your stock broker showing how many RSU's you have vested so far versus ones that are scheduled to vest over the next X years.
For a bonus: rather than liquidating all your vested RSU's for the downpayment, hold onto a good number of RSU's in your brokerage account as these can be used to show you are holding assets, which can help you get a lower mortgage rate as well. Banks love to see that you have assets you are holding onto and can liquidate just in case you do need cash. Their ideal customer is someone who can technically buy a house in cash, but is only applying for the mortgage because the mortgage rates are currently lower than the stock return rates.
Chances are if you work at FAANG and have RSU's that's actually considered a very safe loan that you are basically guaranteed to be approved for at a very nice low mortgage rate. You'll be able to get approved by multiple banks, and then get them to compete with each other to lower their rates by fractions of a percent to try to win your mortgage agreement. Mortgage brokers are your friends here, pay one to do the hard work of contacting the banks on your behalf and make sure your documents look good and then the banks will be falling over themselves to give you a loan.