Is it possible to create cellular organisms out of nothing?

Yes, it's definitely possible. That's how the very first cells were formed - theory known as abiogenesis.

What inspired your question?

The main and most unique characteristic of cells and other organisms is the ability to reproduce (using materials from the environment). Reproduction is the production of exact copies of the initial organism (the copies must be able to reproduce as well).

It is generally accepted (and very logical) that at least the first reproductive "organism" was created from raw materials. It is possible that this "organism" was not a cell, but a unique molecule with the ability to create copies of itself. The process of reproduction was just some chemical reactions. That was the big step that slowly led to the creation of more complex molecules and finally the cell.

If reproduction is enough to name something an "organism", then it shouldn't be too hard to create artificial "organisms" (though they will probably be completely different from the life forms we know.) For example, a machine that is able to reproduce itself (create perfect copies of itself) could be called an "organism". It's energy source could be electricity (from a power source, or the sun etc) instead of glucose. It could also be using materials like iron etc instead of proteins and others that are used by cells.

So, in a sense, a machine with the ability to reproduce is not so different from a cell.
However, we still have lots to learn before we create actual cells with DNA, membranes, organelles etc.

To return to your question, the answer is yes, it probably is possible for organisms to be created from nothing, and earth organisms are the perfect examples. However, the events that must occur are so improbable that a huge amount of time is likely to pass until an organism is created (if it is created). So, it's not very likely to observe the creation of an organism from nothing any time soon without the help of humans.