After Witold Pilecki infiltrated and set up a resistance organisation the idea was discussed in the Home Army, but rejected; The book Fighting Auschwitz by Jozef Garlinski cites the 1942 garrison of the camp as 3,250 soldiers, of whom 120 were officers, and goes on to state; "In 1943 it was at least about the same. Besides, if open fighting broke out, the SS could get assistance from the German units stationed not far from the camp. Even if a surprise attack were successful and the camp were opened up for a few hours, what would happen to the many thousands of prisoners freed for a short time? On April 25th, 1943, the men's camp with Birkenau and the nearby sub-camps, numbered 46,055 prisoners and about 10,000 women. 35 a large percentage of them were not only unable to walk far but in need of immediate medical and hospital treatment. An attack on the camp with any hope of success, i.e. rescue for prisoners, would only be possible within the framework of a country-wide rising, at the time when the Occupation began to disintegrate."
Supplementary questions:
Were the Polish resistance aware of the concentration and extermination camps and their purpose?
Would the Polish have cared about what was going on in those camps?
The garrison expanded with the size of the camp, which is why it is estimate at 700 SS-guards in 1941, 2 thousand in June 1942, about 3 thousand in April 1944, and about 3,300 SS men and female overseers in August 1944. The peak figure was in connection to the death marches when the camp was dissolved in mid-January 1945 and numbered 4,480 SS men and 71 female SS supervisors there. According to the Auschwitz memorial, throughout the entire period that the camp was in existence, a total of some 8,000 to 8,200 SS men and some 200 female guards served in the garrison.
Now, the Armija Krajowa (Home Army) was actually the largest or second largest (it is hard to say exactly) resistance movement in Europe during WWII with the common figure usually cited of about 400.000 members in 1944. And while it did fight several full scale battles against the Germans like Operation Tannenberg in 1944 when its units cooperated with the Red Army on a tactical level, the logistics and consequences of liberating Auschwitz would have made such an operation all but impossible.
At any point in time of its existence, Auschwitz housed several thousand prisoners with e.g. in 1944 at least 40.000 Hungarian Jews deported there that year. The vast majority of these prisoners was not in very good physical condition and required – as the post-liberation period in 1945 showed – extensive medical care, especially in regards to nursing people back to health after starvation and disease.
The AK and the communist Polish partisans saved thousands of individual Jews over the years of their existence from the Nazis. They even went as far as to purposefully infiltrate the Auschwitz camp to report on its internal conditions to the Polish government in exile in London.
But a task so momentous such as caring for tens of thousands of liberated prisoners from the Auschwitz camp, especially with hygienic and medical conditions in the camp was beyond them. It was beyond the US and British Armies in the first week after liberation as the experience of Belsen showed – and those not only had to not fight anymore at this point but also had a whole infrastructure and might of the logistic, medical and industrial capabilities behind them in probably one of the greatest medical and refugee care operations in the history of humanity.
So while form a purely military standpoint, it might have been possible to liberate the camps, the Polish partisans simply did not have the capabilities to care for and save its inmates under the given and existing conditions.
The only camp liberated by a Partisan force while WWII was till going on was the Italian Camp on the island of Rab. But that is a bit different in some ways, not only in that not being a German Concentration Camp. After Italy signed the armistice with the Allies in September 1943 and dropped out of the war, the area was officially taken over by the Germans but the Partisans managed to send several boats to the island, effectively liberating the prisoners healthy enough to still walk and take part in the fight under the eyes of Italian guards that effectively just stood by. Several hundred Jews who had been imprisoned there also joined the Partisans with their unit, the Rab Battalion. But that is just fundamentally different from liberating the biggest Nazi camp complex in all of Europe.