No I wouldn't try anything just yet, give him a few days to get over the jet lag, and just get some sleep into you all as best you can. But then get started - the sooner you tackle this, the sooner you all should be able to get some better sleep
What you may need to do if every day is totally different is take an approach Tracy recommended for establishing a routine for the first time. It can be quite tough but what she suggested was sticking rigidly to set times for WU, naps and BT for several days to set LOs body clock. You might find this link helpful:
Starting E.A.S.Y. at Four Months or Older. You wouldn't use the four hour routine suggested in the link as that would be more appropriate for a four month old baby, but rather aim for something like:
WU 7am
Nap 9.30am for 1.5-2h
Nap 2/2.30 (3h after first nap ends) for 1.5-2h
BT 7pm
Or you can look here:
Sample EASY Routines from 0 - 13mths+ for some other suggestions, bearing in mind that a two nap routine is likely the most appropriate to aim for at this age.
If you could plan to start on a day where you can stay home for 2-3 days instead of having to make trips out that would probably be the best option. Start first thing in the morning and be consistent with PUPD for all naps, BT and NWs. For naps you try for 45 minutes before taking a short break, feed if you need to (don't let him fall asleep - if he is dozing, sit him straight up) and them go back to PUPD for the rest of naptime. At BT and NWs you do it for as long as it takes for him to go to sleep.
Have a look here to ensure you are doing PUPD in an age-appropriate way:
How to PU/PD (inc age adaptations)I'd also suggest you make yourself a plan for overnight feeds. If he is used to nursing frequently at night it is a bit tough on him to go straight to no feeds - and it would be entirely reasonable for him to still need one or two night feeds at this age. What I would suggest is to note the time his BT feed starts (e.g. 6.30pm) and then make a note of 4h later (10.30pm). If he has a NW, check the time - is it before 10.30pm? If yes, then use PUPD to get him back to sleep. All the way to sleep, even if it takes you past 10.30pm. He has to learn that protesting for long enough does not lead to mum and dad giving in and feeding him - that just reinforces the prop. If it's after 10.30pm when he first wakes, then note the time, feed him immediately and put him back down. It is ok to feed to sleep on these occasions, but if he needs help settling use PUPD as before. Next time he wakes do the same - has it been 4h yet?
The first few days will be tough, but the more consistent you are, the quicker he will get it. It is normal for LOs to have very short naps or even no naps the first day or so, but at some point the fact they are so exhausted starts to work in your favour as LO will just not be able to fight sleep any more.
How do you feel about all of that?