Is the Amtrak station close by the zoo?

Not sure. I'm not from the area.

The 11 bus drops you right in front. I believe the 62 drops you in the front of park and you have to walk 13-15 mi uses to where the zoo is located. I learned this on my last visit as we tried the bus and scooters instead of driving. But we did not take the 62 (I may have that bus line number confused, but one drops you right in front which is the 11 that we took and the other almost 15 minutes away).

I will say not to close. Amtrak is more downtown by old Sacramento. But from the zoo it may take 10 minutes to get there by car or less spending on the traffic.

The Amtrak station is a bit less than 4.5 miles from the zoo! Sacramento Valley Station - 401 I St