Both times I went straight up. First time I flew overnight from australia, spent the day in tokyo, bus out in the afternoon and started about 8pm and got destroyed by a storm about 2/3's of the way up. Bit of a disaster really as we weren't well prepared (it was one of those things we decided to do in the pub a few days before the trip).

Second time we were out of season and left about 9. We were being dropped off at kawaguchiko 5th station by a member of our group who had done a knee a few weeks before the trip so when we got to the toll gate just after 8pm the guys there told us it was a 45 minute drive each way and they were closing the gate at 9pm so we didn't have enough time. We explained we were the nissan sports car club from australia, were driving a nissan and would be just fine (made it by about 10 minutes). We started that night just before 9, had a pretty relaxed walk up with a couple of decent stops along the way and had around an hour up top waiting for sunrise

At the spots where the huts are there will be an area you can sit down and eat some food. You can buy hot noodles and the like on the way up but iirc the huts higher up only sell hot food to those staying (happy to be corrected on that one). That said, if you're not staying in a hut I would plan to carry the food you want to eat and treat anything hot you can get as a bonus. If you do walk up I would plan to get to the summit an hour or so before sunrise to beat the crowds which pour out of the huts as the trail can turn into a pretty tedious queue