I know this doesn't directly get at profitability, but your question had me thinking. From Uber's latest 10-Q [1], we know that their "gross bookings per trip" is ~$15/trip. If we use this as a benchmark, Waymo’s 100,000 fully autonomous rides per week would generate roughly $1.5 million per week or $78 million in ARR.
But it's a huge stretch to compare these apples-to-apples. It's just the closest thing I can think of to anchor to. The cost structures could be markedly different (since Waymo directly owns and operates its fleet, and bears direct costs for vehicle depreciation, maintenance, insurance, and the whole tech stack enabling autonomy). Right now those fixed and variable costs are likely higher than Uber's (which only take commission on rides while drivers bear the opex).
[1] See pg. 36 (https://d18rn0p25nwr6d.cloudfront.net/CIK-0001543151/ca7e58c...)