Does the delayed burial of Jesus attest to the fact that he had no close relatives other than his mother?

Before going into this question let us first see what St. John states in his Gospel. St. John was the only Apostle to witness the Crucifix of Jesus. The others had abandoned Jesus through fear of the Roman and Jewish authorities.

30 Jesus therefore, when he had taken the vinegar, said: It is consummated. And bowing his head, he gave up the ghost.

31 Then the Jews, (because it was the parasceve,) that the bodies might not remain on the cross on the sabbath day, (for that was a great sabbath day,) besought Pilate that their legs might be broken, and that they might be taken away.

32 The soldiers therefore came; and they broke the legs of the first, and of the other that was crucified with him.

33 But after they were come to Jesus, when they saw that he was already dead, they did not break his legs.

34 But one of the soldiers with a spear opened his side, and immediately there came out blood and water.

35 And he that saw it, hath given testimony, and his testimony is true. And he knoweth that he saith true; that you also may believe.

36 For these things were done, that the scripture might be fulfilled: You shall not break a bone of him.

37 And again another scripture saith: They shall look on him whom they pierced.

38 And after these things, Joseph of Arimathea (because he was a disciple of Jesus, but secretly for fear of the Jews) besought Pilate that he might take away the body of Jesus. And Pilate gave leave. He came therefore, and took the body of Jesus.

39 And Nicodemus also came, (he who at the first came to Jesus by night,) bringing a mixture of myrrh and aloes, about an hundred pound weight.

40 They took therefore the body of Jesus, and bound it in linen cloths, with the spices, as the manner of the Jews is to bury.

41 Now there was in the place where he was crucified, a garden; and in the garden a new sepulchre, wherein no man yet had been laid.

42 There, therefore, because of the parasceve of the Jews, they laid Jesus, because the sepulchre was nigh at hand. - John 19: 30-42

St. John seems clearly to imply that the burial of Jesus was hastily done and that Our Lord was buried in a tomb that was close at hand because of convenience.

In order to prepare the body of Jesus before sundown, those who remained present at his Crucifixion had a mere three hours tops, to place his sacred body into the tomb. That includes taking his body down from the Cross, transporting it to the burial site, preparing to body for burial and then sealing the tomb with the heavy rock.

So in actuality, there was no delay in the burial of Jesus. The basic assumption that there was is false. And this can not attest in any manner whatsoever to the fact that he had no close relatives other than his mother, whether cousins or other close relatives.

Besides, who could have known the placement of Our Lord Crucifixion other than God himself. Three hours between Jesus’ death and burial is very extremely time limited.

Furthermore, the Catechism of the Catholic Church explicitly mention this fact as do the Gospels (Cf Lk 24:9-10; Mt 28:9-10; Jn 20:11-18).

The empty tomb

640 "Why do you seek the living among the dead? He is not here, but has risen."493 The first element we encounter in the framework of the Easter events is the empty tomb. In itself it is not a direct proof of Resurrection; the absence of Christ's body from the tomb could be explained otherwise. Nonetheless the empty tomb was still an essential sign for all. Its discovery by the disciples was the first step toward recognizing the very fact of the Resurrection. This was the case, first with the holy women, and then with Peter. The disciple "whom Jesus loved" affirmed that when he entered the empty tomb and discovered "the linen cloths lying there", "he saw and believed". This suggests that he realized from the empty tomb's condition that the absence of Jesus' body could not have been of human doing and that Jesus had not simply returned to earthly life as had been the case with Lazarus.

The appearances of the Risen One

641 Mary Magdalene and the holy women who came to finish anointing the body of Jesus, which had been buried in haste because the Sabbath began on the evening of Good Friday, were the first to encounter the Risen One. Thus the women were the first messengers of Christ's Resurrection for the apostles themselves. They were the next to whom Jesus appears: first Peter, then the Twelve. Peter had been called to strengthen the faith of his brothers, and so sees the Risen One before them; it is on the basis of his testimony that the community exclaims: "The Lord has risen indeed, and has appeared to Simon!"