No, spells only do what they say they do
Firebolt’s description reads:
You hurl a mote of fire at a creature or object within range. [...] A flammable object hit by this spell ignites if it isn't being worn or carried.
If you targeted the creature, neither the web nor the creature would not catch on fire. As a creature is either wearing and/or carrying any flammable objects in its possession, they do not ignite on fire. The creature simply takes fire damage.
If however you specifically targeted the 5ft cube of web the creature was in, it would then catch on fire and do 2d4 damage to the creature, as per Web’s spell description:
The webs are flammable. Any 5 foot cube of webs exposed to fire burns away in 1 round, dealing 2d4 fire damage to any creature that starts its turn in the fire.
However, there is a possible way this could happen, albeit via homebrew
If you used the optional rule for Hitting Cover, found on page 272 of the DMG, and treated the web as cover, you could potentially ignite the web by targeting (and missing) the creature.
When a ranged attack misses a target that has cover, you can use this optional rule to determine whether the cover was struck by the attack.
First, determine whether the attack roll would have
hit the protected target without the cover. If the attack roll falls within a range low enough to miss the target but high enough to strike the target if there had been no cover, the object used for cover is struck.
I will point out that this is more of a homebrew use of this optional rule because, as stated previously, spells only do what they say they do, and web says nothing about providing cover.
Alternatively, the DM could simply rule that “because the web is such a huge target, it still lights on fire” or “because the firebolt had to pass through the web to hit the creature, it lights on fire”. Again though, this is a not a Rules as Written ruling.