Is there any way to determine the date a domain DNS record like MX record was published

Short of a kind of crawler that keep historical snapshots like the Wayback Machine but for DNS, no, this is not possible.

If you suspect that the MX record update may have been the most recent change to the DNS zone, then you can always check the zone serial number in the SOA record. One very frequently used convention for the format of the serial number is YYYYmmddnn where nn is a serial number for multiple modifications made on the same day. This might give you a clue as to when the zone was most recently updated. But this convention is not necessarily in use, and it can lie even if it is, and it doesn't tell you what was modified. The only thing I would infer from it is that probably nothing at all has changed in the zone since the date that appears in the SOA. Probably.