I think the early Christians knew, and they wrote about it. What the early Church Elders believed:
Lipsius quotes Iraneus (Bishop of Lyons in 177AD):
"The construction itself of the cross has five ends, two on the vertical and two on the horizontal, and one in the middle where the person attached with nails rested".
Also on page 661 Lipsius has an illustration of a cross with a cross-beam and a foot-rest, upon which a man is nailed, arms outstretched. This is under the heading "De Cruce Liber Secundus".
Irenaeus (early 2nd century – AD 202) remarks that "the very form of the cross, too, has five extremities, two in length, two in breadth, and one in the middle, on which [last] the person rests who is fixed by the nails".
The same remark is made by Justin Martyr (100–165) when commenting on the Book of Deuteronomy 33:17: "For the one beam is placed upright, from which the highest extremity is raised up into a horn, when the other beam is fitted on to it, and the ends appear on both sides as horns joined on to the one horn. And the part which is fixed in the centre, on which are suspended those who are crucified, also stands out like a horn; and it also looks like a horn conjoined and fixed with the other horns".
To the pagan jibe about Christians being devotees of the cross, Tertullian (c. 155 – c. 240) responds by saying the pagans no less adored images of wood, with the difference that they worship what is only part of a cross, while the Christians are credited with "an entire cross complete with a transverse beam and a projecting seat". He then adds that "the very structure of our body suggests the essential and primal outline of a cross. The head ascends to the peak, the spine stands upright, the shoulders traverse the spine. If you position a man with his arms outstretched, you shall have created the image of a cross."
Justin Martyr also states: "That [passover] lamb which was commanded to be wholly roasted was a symbol of the suffering of the cross which Christ would undergo. For the lamb, which is roasted, is roasted and dressed up in the form of the cross. For one spit is transfixed right through from the lower parts up to the head, and one across the back, to which are attached the legs of the lamb.