Q. Ancient synagogues have been discovered and excavated in Israel. Why do there not seem to be the remains of any ancient Arks?
The usual term for the Ark was tevah, literally a chest. The same word is used for the ark in the story of Noah.
The synagogal Ark was originally not a fixed cupboard but a chest containing the scrolls; it was brought into the synagogue when needed for a service. The Mishnah in Ta’anit records that in time of drought the Ark would be taken out into the town square for a communal prayer rally.
The date when the portable Ark was replaced by something more permanent is not certain, but it must have been somewhere in or before the 4th or 5th century CE since the synagogues dating from this period have a recess which must have housed the Ark.
In more recent times, ruined buildings have been found in many places that once boasted Jewish communities, and if there is a doubt as to whether a ruin was actually a synagogue the existence of an apse that must have been where the Ark stood is a decisive argument for the identity of the building.
The question that naturally needs to be asked is what happened to the actual Arks from these buildings and, even more so, what happened to their Torah scrolls.
In some cases they were saved and found new homes. In others they suffered martyrdom. One cannot imagine any Jewish congregation willingly abandoning its Torahs.