Jain tradition does not point to one single “oldest object” that is universally accepted as the very first Jain idol or temple on Earth. What we can say with traditional and scholarly support is:

• The earliest conclusively identifiable Jain surviveable artifacts are ancient Jain sculptures (murti) and inscriptions dating roughly to the early centuries of the common era, with some pieces (especially from Mathura region) often dated around the 1st century BCE to the 2nd century CE. These include images of Tirthankaras in stone that show the early Jain iconographic style.

• Early Jain cave shrines and rock-cut art also appear in this broad time frame, but the specific “oldest” example is not universally fixed in date, and attributions can vary among scholars and among Digambar and Shwetambar traditions.

• The oldest temple sites that are actively associated with Jain worship in many traditions are often cave temples or early masonry shrines, which later underwent extensive rebuilding or expansion. Famous later temple complexes (constructed in the medieval period) include grand sites like Ranakpur, Palitana, and others, but they postdate the earliest artifacts by many centuries.

If you’d like, I can look up more precise scholarly dates and note where Digambar and Shwetambar understandings differ. You can also read more on the JainKnowledge site about early Jain art and architecture.