My little girl sometimes wakes early (occasionally)... what I do, but not as a rule, is go in and tuck her back in. Sometimes (only sometimes) I give that first bottle/milk cup a little earlier and then put her back down.
I know people are probably going to have a go at me saying you never want to feed a baby to sleep and I 100% agree with that, but I just tend to gauge the situation and offer the bottle and then she is sometimes more relaxed and has a bit more sleep. (But not always). I have her bottle and breakfast split anyway - usual bottle is upon wakeup at around 6/6.30 am and then breakfast 1.5-2hrs later.
I would be checking the following as well - is your baby too hold/cold? Is the light all blacked out? (It is winter here but where you are, maybe it is daylight saving time and there is sun creeping through?) Is he eating enough dinner? All obvious things to check, sorry just posted them as reminders!!