Question : How long do most people visit Astana?
Answer : Of course you're not most people, but if you were, you'd stay roughly 21 days.
Question : Is there another local airport that can get you to Astana?
Answer : Departing from Norman Y. Mineta San Jose International Airport is not the only way to get to Astana International Airport. Try searching for flights from San Francisco International Airport (SFO) as well. Over the upcoming two months, flights from SFO to TSE are being booked 10% cheaper than flights from SJC to TSE. Being only 31 miles away, it's easily accessible for most.
Question : If your plans are flexible, have you considered changing your departure day?
Answer : Monday is your cheapest day to fly in the month of July. Flexibility is paramount when booking travel plans in order to keep travel costs down.