Any technology that can travel through time should be able to approach near light speed to catch up to whatever they wanted to. It would be a mild disappointment at worst.
Assuming you head forward in time first. That also makes the assumption that the maker of the time machine considered the possibility that the earth might not be there in that time frame. Or that people in the future actually care or can tell when something pops up.
If nobody returned from time traveling then they could assume that either a law was preventing such or that there was a danger that prevented them. They would send an exploration device to discover such a thing and would undoubtedly realize what was happening.
That makes the assumption that the advance society is testing it. What if it was really created in the 17th century but when the inventor used it he/she died because of the spacial displacement. But for the case of the advanced society with near or actual FTL travel? Spacial movement as we have discussed may not correlate to the current position and time travel may place you where you were for traveling forward and where something will be when traveling in the past. Now that is only presuming that your spacial location is dictated by your starting position. It may require an entirely different set of rules to move through time and not just appear somewhere completely random in the universe. You could go forward in time a day but reappear 10 billion light years away or farther. Or you could appear in the same location as something like a planet or a sun. It may be that you can't do time travel at all in a gravity well or the reverse. Or maybe you can move but can't stop once traveling.
*cough*