You speak correctly when you said that Jesus was homeless. He was homeless by choice. As an itinerate teacher, He traveled about healing, teaching, and living in total obedience and dependency on Father God. His security was in Father God. Not in money or material wealth.
From my up-close observations, most people are homeless because of drug addiction, domestic violence, a lack of education, bad choices, or mental illness. Jesus was not affected by any of these maladies. And do not be too quick to glamorize homelessness.
So should you follow in Jesus’ footsteps and be homeless, too?
Jesus walked on water.
Jesus turned water into wine.
Jesus healed blind people.
Jesus calmed raging storms.
Jesus was born of a virgin.
Jesus lived in Israel.
Jesus raised Himself from the dead.
Jesus was totally dependent upon God.
Jesus did not carry money on His person.
Jesus surrounded himself with fishermen, zealots, tax collectors, and the like.
Jesus was the focal point of the scriptures.
Jesus was and is God.
Learn to do all the other things that He did and then you can consider becoming homeless like Him, too.
Or, you might consider seeking out His perfect will for your life. I cannot see how you can do Him much good sleeping on park benches and foraging for food from dumpsters. Let me suggest that He has other plans for your life. Seek out His will. Consider a good biblical education and enter ministry. For the record, we don’t need any more homeless people, but we can always use qualified Bible teachers or dedicated missionaries!