For me, the first week was definitely the most difficult (both times, had a relapse once after a couple years of sobriety) both physically and mentally. Then the frequent and often unpredictable, intense cravings for alcohol that lasted for months... how to tolerate them and how not to act on them. No recovery program helped me with the cravings, really just had to let it ride its course. Sometimes I had bad anxiety but nowhere near as horrible as during the countless cycles of heavy drinking and short stints of abstinence, and I'd always had anxiety, even before starting to drink, so that was not too hard to manage. In general after the first week, when I was not momentarily flooded by cravings, I was reasonably well. Had other challenges on/off, but I don't think those were related to drinking/sobriety per se, more just general life and the nature of who I am. Several years sober now, I am doing probably the best ever, but it's related to many things including a different lifestyle, significantly increased practical security, and aging (now 45) has also been playing a very positive role for me mentally at least. I've become much less interested in intensity, much less prone to excess and unhealthy-type unconventional patterns.
If I had to name the biggest challenge of early sobriety for me, it would definitely be the monster cravings. They got worse at first for a while but then gradually much lighter and less frequent. If I had to give advice to someone very similar to me, I would suggest that they explore some of the now available medical treatments to potentially ease the cravings in the first months. Maybe they wouldn't work but alleviating even just a bit that torture would be worth the trial for me. Other than that, I had to focus on learning how to reward myself positively and for that, living in an environment that is generally highly stimulating, diverse and compatible with me really helped. I think it would have been much harder being in a life condition that I did not like although probably not impossible.