She went to sleep.
to inf. : She went (somewhere) in order to sleep.
preposition to : She fell asleep.
Which one is more likely at the first glance of the sentence above if you are a native English speaker?
It almost always means that in any context unless otherwise stated (eg 'she went to sleep at her friend's house').
Don't compare it to "go to work", because work is more often than not a physical place away from the home that you 'go' to, whereas 'sleep' is a state, not a physical place. Most people would say "she went to bed" to mean the act of physically taking yourself somewhere to sleep.