Early Christians were reluctant to depict the crucifixion of Jesus Christ. Some scholars believe this reluctance persisted well into the 4th or 5th century.
We must always remember that ideas and symbols are often present for a long time before they become popular and are recognized publicly. Tertullian, writing around 200AD, said that Christians wore their foreheads out with the mark of the cross. So, whether we can find a symbol somewhere or not to date back to the early Church we know it was a common behavior.
Its unlikely that Christians rejected the cross in the early years because they then would have had to hide the fact that Christ was crucified. Which they didn’t. So the argument for a later dating of the cross symbol doesn’t make theological or evangelical sense. The epistles of Paul also speak of Christ and him crucified. Even Christ himself said we must pick up our cross daily and follow him.