Would men have ever sinned if Satan did not tempt Eve in the garden in the first place?

It is possible in my opinion that Adam and Eve were destined to sin by being tempted by the Devil. At least in Gods eyes they would have been, as he knows all things past, present and future. I am suggesting Adam and Eve were fulfilling prophesy.

I believe that in this physical life we are experiencing, struggle is necessary for spiritual growth. Living blissfully unaware that we have more than the one right option in any situation might sound great to some, but eating from the tree of the knowledge of good and evil was necessary to truly receive the gift of choice and free will. Redemption is key to spiritual growth and this was made possible by Jesus sacrifice.

There is a basic concept that you appear to be overlooking. Satan is eternal. God never totally destroys any of his creations, which have life given by him. He only destroys Heaven and Earth in Revelation Chapter 21 verse one.

That Heaven that is destroyed is the heaven we know as our atmosphere. The Heaven we aspire to is eternal, and all things that were created for that Heaven are also eternal, whether or not they end up there.

Consider the following verses from the Revelation:

Revelation 19:20 KJV And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone.

Note that it says that they were cast alive. that tells us two important things. That both beast and the false prophet have life. A large part of God's punishment is eternal pain and suffering, as we see in the following verse:

Revelation 20:10 KJV And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.

Here we find that Satan is also going to be tormented forever. There will be no lessening of that torture and there will be no end to it. And they will never be completely destroyed, since death will have been eradicated.

Revelation 20:14 KJV And death and hell were cast into the lake of fire. This is the second death.

Now as to whether or not man would have sinned if Satan were not there to tempt Adam and Eve. The only Angels left in Heaven are those who chose to reject Satan and his Dominion. When God created mankind he gave us that same choice that the Angels had, that of choosing between two eternal destinations. Satan and the fallen Angels could have chosen to remain in Heaven under God's rule, instead of rebelling, and we have that same choice. It was not Satan who made them sin, it was the choice they made to disobey God. That within itself is the sin which doomed all who followed them.

Would they have eaten from the tree had Satan not tempted them, we cannot know the answer to that question, but God knew that unless they were in some way tempted they would not exercise their free will. Satan was only doing God's will, in tempting them even if he did not know it at the time.

And there is one more thing to consider, that being that unless we make the right choice, we will suffer that same punishment that God initiated for Satan and his minions.

Revelation 20:15 KJV And whosoever was not found written in the book of life was cast into the lake of fire.

The Book of Life is a list of those who have chosen God as their King rather than Satan. At this point I would like to say that living a life in worship of God; whether or not God actually does exist (of which I personally have no doubt) only makes sense in light of the probability that Every Word of the Bible, is actually the word of a living God. Believing in God in that case is far more desirable than the alternative.