As other people mentioned, you can take the first MRT train and reach airport in time
If you really want to save money on hotel and transportation:
Night before, take MRT and reach before midnight. CA allows early check-in with bag drop from 6am-2359. Snooze in a lounge (some lounges are very strict about 3hr limit,some aren't). I've done it for a 6am flight
If you want a good night's sleep but save on transportation: arrive at airport the night before.Rent a room (60-150) at the transit hotel
Transit Hotels | Changi Airport Singapore