We are taught that when we came to Israel, King David could not build the temple because he had blood on his hands. Though he was acting under divine command and in the interest of the nation, he still was not allowed to undertake this task. Solomon was given that responsibility and he ultimately completed it.
My question relates to the reasoning for David's inability to build the temple.
In the event that we did decide to build the third temple, would the issue of bloodshed or other impurities come up in the vetting of those who would build the temple?
My assumption is that some level of ritual purity "standard" would need to exist. What that standard is and how we would come to a determination for who does or doesn't qualify is beyond my knowledge. I simply relate this to how there are certain areas of the Beit Hamikdash which only the priests could enter. This makes me think the entire process would need to be overseen by authorities to maintain a baseline "purity" for the entire location during the building process.
Is there any sort of standard we know of regarding what qualifies or disqualifies the would-be builders of the third temple?
Has such a standard or process even been theorized in Jewish sources? Or is it so oddly specific that no one ever considered how we might begin such a process?