No; Eldritch Cannon doesn't get rid of the spell slot cost
The Artillerist artificer gets the Eldritch Cannon feature at 3rd level when they choose the subclass, which lets them create an eldritch cannon. The feature says, in part (Eberron: Rising from the Last War, p. 59; emphasis mine):
At 3rd level, you learn how to create a magical cannon. Using woodcarver’s tools or smith’s tools, you can take an action to magically create a Small or Tiny eldritch cannon [...]
Once you create a cannon, you can’t do so again until you finish a long rest or until you expend a spell slot of 1st level or higher. You can have only one cannon at a time and can’t create one while your cannon is present.
Rules designer Jeremy Crawford unofficially clarified in a November 2019 tweet about the Eldritch Cannon feature that the spell slot needed to be expended specifically to create the cannon (not just incidentally as part of some other use).
At 15th level, Artillerists get the Fortified Position feature, the second benefit of which reads (p. 60; emphasis mine):
You can now have two cannons at the same time. You can create two with the same action (but not the same spell slot), and you can activate both of them with the same bonus action. You determine whether the cannons are identical to each other or different. You can’t create a third cannon while you have two.
This parenthetical clarifies that you can use the same action to make 2 cannons, but it doesn't expend "the same spell slot". Given that the Fortified Position feature specifically indicates that expending a spell slot to create one cannon for it doesn't give you the second cannon for free (i.e. without expending a spell slot), making your first cannon of the day for free wouldn't allow you to ignore the spell slot cost either.
The Eldritch Cannon feature initially grants you the ability to make one cannon, and you can't make another one until you take a long rest or you expend a spell slot to make one. The fact that you can now make 2 turrets with 1 action doesn't tell you that you suddenly ignore the cost of additional turrets beyond the first. The fact that it explicitly calls out that it doesn't ignore the spell slot cost further supports the idea that additional turrets beyond the first are not free.
Essentially, you don't have the ability to make a second turret for free to begin with - and this feature doesn't give that ability to you, so you can't do it. You can simply make one cannon of the day for free and expend a spell slot for a second one, using a single action to make both.