Dear katdan,
I know nothing about how the seamless robe Jesus wore was made, but I do know that a knitted sock is also seamless. The making of a seamless garment could be either as in knitting or crocheting weaving continuously with a single strand and catching in the previous 'round' as one goes, or, by joining the beginning to the end of the threads which run up and down a piece of cloth, normally, and then weaving across them backwards and forwards, slowly edging the woven part away to bring new 'open' threads into line with the shuttle. (Am I making sense?) Eventually, it would not be possible to fit in any more rows with the shuttle, and just one end would need to be finished off - possibly by attaching it to the beginning.
Does this in any way answer your question?
I feel sure it would be possible to commission a seamless tube without the use of computer, as long as you found someone with a loom of the correct size.
Many sweatshirts and Tshirts are basically a knitted tube, these days, with holes cut out for the sleeves, and a seam over the shoulders to close it up towards the neck.