There are two issues with your question that both lead to potential answers.
First, the assumption that there was ever "a first cell" is wrong. Life in general occurs in populations; if there's one of something then there usually are others. And the same is true in chemistry; usually if you have a certain molecule in a certain place there are probably others there too (that got there in the same way the first one did), and they're all having similar reactions (because similar molecules behave in similar ways). As abiogenesis, the general term for the development of life from non-life, involves complex chemistry resulting in self-replicating systems resulting in life as we know it, all of those principles would apply there too.
Second, the assumption that the first life was a cell is likely wrong (except if God created life, and started with a cell, or some other such ad-hoc idea of course). Life is partly defined by self-replication, and self-replication is also what allows the optimization of systems for specific purposes via the processes of biological evolution (which requires, and is a consequence of, imperfect replication); meaning that as soon as you get a self-replicating system you're well on your way to having life - and the first cells as we know them likely developed quite far along that process, because they already are quite optimized.
In this perspective, the answer to your question is that there was never an issue of "the first cell" "deciding" to "replicate" - the first life replicated by definition - and whether it was a cell or not is a completely different issue.
As to how the first life "decided" to replicate - replication is a chemical reaction, it's not like modern DNA "decides" to replicate, it is a chemical reaction that occurs when the conditions make it inevitable. Biologists currently do not know what the first self-replicating molecules or systems were and how they replicated without the complex mechanisms that allow the chemical reactions that make DNA replicate, but the assumption is that it was a chemical reaction that happened for the reason chemical reactions happen - the components and conditions are such that following the laws of physics results in the chemical reaction happening. For what it's worth though it should be noted that while DNA cannot do anything outside of the mechanisms of the cell, the same isn't true of RNA; in fact small sequences of RNA can pair off on their own in solution, and it is generally thought that RNA came before DNA in the development of life.
Abiogenesis is an unanswered question of science, but if you want more ideas of what biologists think might have happened you could look here:
Otherwise I can't help but mention my favorite hypothesis of abiogenesis, which I find most exciting and (to my layperson eyes) convincing, and more importantly illustrates how "the first cell" could have been a fairly late step in the development of life. Here is a video of one of its originators talking about it:
Basically those researchers started out looking at the energy of the chemical reactions that make the building blocks of life, and figuring out how natural reactions could generate that energy. They found that the conditions that occurred in hydrothermal vents were conducive to such reactions:
In more recent papers they connect this to comparisons of existing cells to try and figure out which features the Last Universal Common Ancestor of all life had, and putting those things together they build a fairly coherent picture of the first "organisms" developing inside pores of the material of hydrothermal vents, involving chemical reactions that produced complex molecules which promoted the production of further such molecules (including proteins, enzymes and RNA that can both self-replicate and promote the creation of proteins), and the development of membranes not so much as a protection from the outside world but to maintain the energy difference between inside and outside the pores ("proton gradients") that further promoted the reactions in question, and bacteria and archae being the result of two independent events of cells "breaking off" from the porous rock and becoming free-living.
Here is a figure from that paper:
(And this goes a bit to my first point about there not having been a single first cell - you can see in this hypothesis there would have been many pores/reactions occurring along proton gradients/groups of complex molecules reacting in positive feedback loops/self-replicating systems/membranes forming/cells breaking off/etc at any one time, making it more likely for any one "step forward" (in quotes because it's only a step "forward" in hindsight; at the time it would be a variation among others) to occur somewhere in that population).