How much time would it take to grow enough plants on Mars so that it would create enough oxygen for animals, organisms and humans breath without the aid of an enclosed ecosystem?

The bigger problem is the lack of water on Mars. Hard to grow plants with no water. Yes, there’s some water on Mars, but not anywhere near enough to grow and sustain sufficient plant life.

Like @Darth_Algar said they need water,and how hard it will be to access the amount needed to grow enough plant growth,to create an atmosphere that can sustain life.

A very long time. Plants are very good at being carbon neutral, the oxygen they produce almost exactly offsets the oxygen they use to stay alive. Most of the earths oxygen comes from phytoplankton in the oceans.

The prospects of terraforming Mars other than under some form of enclosed space are pretty bleak with the technology available to us today. Mars is further from the sun than the earth, but lacks the earth’s powerful magnetic field to deflect the lethal radiation deadly to multicellular organisms. In addition mars has only 38% of earth’s gravity, which means the lighter gasses captive in our own atmosphere are much more susceptible to escape. Plants do generate oxygen, but do so by “inhaling” carbon dioxide, separating the molecule, holding on to the carbon and “exhaling” oxygen. Our own plants required billions of years to convert our lethal atmosphere to breathable air, and our atmosphere at one time had a much greater percentage of oxygen than today, which was why there so many giant insects. Mars has virtually no atmosphere, and therefore no carbon dioxide for plants to inhale. Of course with genetic engineering, perhaps we design single celled organisms to extract the oxygen from compounds in martian rocks and minerals.

Aerospace engineer Robert Zubrin, in his 1996 book “The Case for Mars,” proposed the following time-table (ref) in a 2004 interview. The answer to OP is in #4:

RZ: If one considers the problem of terraforming Mars from the point of view of current technology, the scenario looks like this:

1. A century to settle Mars and create a substantial local industrial capability and population.

2. A half century producing fluorocarbon gases (like CF4) to warm the planet by ~10 C.

3. A half century for CO2 to outgas from the soil under the impetus of the fluorocarbon gases, thickening the atmosphere to 0.2 to 0.3 bar, and raising the planetary temperature a further 40 C. This will cause water to melt out of the permafrost, and rivers to flow and rain to fall. Radiation doses on the surface will also be greatly reduced. Under these conditions, with active human help, first photosynthetic microbes and then ever more complex plants could be spread over the planet, as they would be able to grow in the open. Humans on Mars in this stage would no longer need pressure suits, just oxygen masks, and very large domed cities could be built, as the domes would no longer need to contain pressure greater than the outside environment.

4. Over a period of about a thousand years, human-disseminated and harvested plants would be able to put ~150 mbar (millibars) of oxygen in the Martian atmosphere. Once this occurs, humans and other animals will be able to live on Mars in the open, and the world will become fully alive.

That’s the scenario, using current technological approaches. However technology is advancing, and 23rd Century humans will not conduct their projects using 21st Century means. They will use 23rd Century means and accomplish the job much faster than anyone today can suppose…

Colonizing mars is a losing battle. Strangely enough Venus is a better prospect.