At level 2 we can obtain mini stat ups with 2 fights. This actually works out perfect since we are likely to need 2 humours still from the level 1 dungeon. This mini stat up phase will also determine what we will gain in the next boss fight, so this is a good way to double up on a strength increase early on.
In theory we can save at least 1 battle if not 2 if we obtain at least one humour from the Level 1 dungeon. Those drops are unlikely however, as it's uncommon to find a Beach Bum encounter as part of the Komodo Dragon pups. At least one fight is usually necessary, so we will go under the assumption (a pretty safe one) that we will end up with 1 extra fight to get the 2 battles necessary here. Also for the sake of comparison, we will assume that it is actually 1 1/2 battles for determining time since if we come for an extra humour with Leena and a MagmaBomb, we end this fight in 1 round (generally). If we make the assumption that a fight takes 30-40 seconds (round numbers), and take the 40 seconds for the worst case we are basically assuming we are adding 60 seconds to get the extra stat up.
Well, it turns out strength upgrades are extremely useful. That is my whole basis for this strategy. Also since we are very early in the run, this is a good time to reset if we are pushing for WR or a general PB. This should be about 15-18 minutes into the run by now, so a reset isn't the worst thing in the world.
Getting an extra strength upgrade here also helps make the next fight faster, which already helps gain some of the time back. Add that to the fact that if you get a strength upgrade in the mini stat up, you will be guaranteed to get a strength upgrade for the Kid fight. This basically acts as a +2 strength upgrade, which is the max you can get for a strength upgrade on a level up. Given how much fights change depending on the strength value of Serge, adding 1 extra strength can save a round on several fights, making the 1 minute (worst case) time loss easily recoverable, and the runs more consistent.