You can "in some cases", according to Book flights on Google support page:
When searching for flights on Google, you'll usually have the option to book with an airline or online travel agency by going to their website. In some cases, you’ll be able to "Book on Google," completing your transaction with the airline or travel agency while staying on Google.
How to book flights on Google:
Search for flights on Google.
After selecting a flight, choose the “Book on Google” option, if available.
Enter passenger details, including name, gender, telephone number, birthdate, and email address. Select Continue.
Choose a stored payment method or enter a new one, then select Continue.
Review your personal details and flight itinerary, making sure they’re correct.
If available, under Baggage, review the disclaimer. If you’d like to add baggage to your reservation, select Add bags.
Add the number and type of bags you’d like for each passenger, and click Done.
To process your payment and complete your reservation, select Book.
If you can't see "Book on Google" option then it seems that you have to make a reservation through airline or travel agency.