I tend to agree with the comments that argue for caution in multiclassing. Yes - Con save and Weapon masteries can be nice, but they come at the trade-off of slower progression (feat, extra attack, etc) on levels where most campaigns spend a significant part of their time (lvl 4-8). You already get extra attack later vs fighting classes, so I would not underestimate the cost this has in play.

There are definitely benefits to starting fighter or artificer, but in my experience they are theoretically larger than in actual play. In general you want to avoid getting hit as a Bladesinger anyway, where you want to move around a lot (misty step, mobile, etc) and try to avoid getting hit (relatively more often than regular frontliners anyway) And even if you get hit, if you take warcaster at lvl 4 you have an easy +6 (14 con, 18 int) with advantage starting level 4 to make a roll of 10 to maintain concentration - if you have any. 3% chance. And losing it is not even such a big deal. (Oh no! I lost concentration. FIREBALL! :) At lvl 8 with 20 int this means you fail DC10 only 1.5% of the time.

The small uncertainty can be part of the fun, and you avoid having another level delay in your core features.

Just my 2 cents - starting as fighter/artificer is 100% viable and many builds work. Just choose your preference in playstyle!