Word iShTaka & its homologs need some discussion. First, it is attested in Iranic e.g. Avestan iShtya & zemo-iStva, zemo=earth ->SKT: jmA; hence, earthen-brick. It is seen in some Dravidian languages in form close to the prAkR^ita one (iTTa-) & the Thai language of Kra-Dai family. Hence, it can be reasoned that it is a widely travelled word that moved along with this technology.
Now, given that Dravidian forms resemble prAkR^ita we can posit a transfer from IA->Dr. Similarly a prAkR^itic form was likely carried to Thailand via trade from India.
Now if it was only found in IA then we could have said that it was borrowed from Harappan as they were prolific makers & users of bricks. However, its presence in steppe Iranian suggests that I-Ir knew it even before they arrived in India. But here is where it gets complicated. It is widely attested in the shruti but not in its vast earliest layer - the RV. This would suggest that it was acquired from some source after the core RV was composed. That’s one of the arguments for why RV was not composed in India or after filtering through BMAC where bricks were widely used.+++(5)+++
So the alternative proposal has been that it was acquired from BMAC after core RV was composed as the Arya-s were moving south. However, there are some complications even here. We have homologs in Tocharian: 1. ishchake= mud; 2 ishchem=brick; ishchemaShShe= earthen (ware)=pottery. The early Tocharianists thought ishchake was borrowing from I-Ir as they moved east or some thought it was an independent BMAC->Tocharian. However, the discovery of multiple Tocharian forms that indicate the raw material mud & other mudware unlike I-Ir, especially with forms like zemo-iShtva where a redundant earthen is added suggest that Tocharian did not borrow it from I-Ir but had it independently with deeper roots.
Tocharian also has aise for pot which is believed to be related to Germanic Essa for kiln/forge. Could that also be related? In that case an Indo-European origin for the word as original meaning mud/clay that was baked into ceramics & later into bricks is a possibility.
Alternatively, like it travelled with the technology in later times, into other languages, it is possible that it originated in some urban culture.