Put them to bed whenever you like and whatever works for them.
But if they're awake for more than 1.5 - 2 hours at that age, they will be overtired and find it difficult to go to sleep. That could be the problem. I'd try rocking/feeding/whatever to sleep an hour and a quarter or so after he last woke up. He doesn't have to be 'in bed' - the advice is that till 6 months they sleep in the same room as you anyway.
We had a 'bedtime routine' from about 3 months at whatever time DS wanted to sleep which was round about my bedtime - the time varied wildly. The 'routine' was to change his nappy in a dim room rather than the light, and feed him in the dark. We tried the whole bath etc but he just got overtired and screamy.
It's also normal for young babies not to properly sleep in the evening and just cluster feed on and off for what might be hours. Don't worry - it does pass - and just keep feeding every time he's giving hunger cues.
Many babies will naturally want to go to sleep for the night quite late at first, but it then becomes earlier - often around 4 months (later in babies who have colic). This is because it takes a while for their biological clocks to mature.
Day & night organisation only really gets going for many babies around 6-8 weeks so you're only at the very start of this. Give it another month or two and you'll find it's completely different. :)
And what I've read suggests that it's only from 3-4 months that babies are able to start to remember things like routines, ie that after bath comes bed. IMO it's not until around 5-6 months that the bedtime routine becomes really useful for baby knowing that they're supposed to go to sleep then. Of course, there's nothing wrong with starting one now if it helps you, but if it doesn't, try again at some point in the future if you want to.