After studying the Old Testament of the Bible, which describes how the Israelite people (ancestors of Jews) were in slavery in Egypt for over 300 years, I believe that the pyramids could have likely been at least partially built by the ancient Hebrews, as slaves.
Here's some examples of the time period when the Israelites were slaves and could've possibly built the pyramids:
"During that long period, the king of Egypt died. The Israelites groaned in their slavery and cried out, and their cry for help because of their slavery went up to God."--Exodus 2:23
"The Lord said, “I have indeed seen the misery of my people in Egypt. I have heard them crying out because of their slave drivers, and I am concerned about their suffering."--Exodus 3:7
“Therefore, say to the Israelites: ‘I am the Lord, and I will bring you out from under the yoke of the Egyptians. I will free you from being slaves to them, and I will redeem you with an outstretched arm and with mighty acts of judgment."--Exodus 6:6
“I am the Lord your God, who brought you out of Egypt, out of the land of slavery."--Exodus 20:2
I know that I'm mostly answering the question of "who" built the pyramids, rather than the "how," but I also think that the pyramids were most likely built by hand, the large stones being put into place by ropes & pulleys, especially considering that the Israelites were in slavery for 300 years, and there were a few MILLION of them! I think given enough time and hands, which they had, that it wouldn't be too much of a stretch to say that they could've been built by hand.
**This was a great question, by the way!**