While I wouldn't call this "evidence", it certainly adds credence to the date, as it's very possible that Sony might have chosen this specific date to pay homage to the game that launched the series.
Although Sony has yet to confirm anything, a brief update to the game's PlayStation store page claims that God of War will release on March 22, 2018.
According to Google Cache, the PlayStation Store listed God of War with a placeholder release date of December 31, 2018 release date up until December 3, meaning the change was applied today. One of those (if not the biggest) is Sony's God of War - the fifth instalment in the long-running franchise that is looking to act as a soft-reboot of sorts. Every mainline entry has had a March release. We hope to get more details during this week.
At the moment, neither site have any pre-order bonuses for the game. A new main weapon and new abilities retain the defining spirit of God of War while presenting a vision of violent conflict that forges new ground in the genre.
KitGuru Says: Sony Santa Monica is taking God of War in a brand new direction with this game and judging by the trailers, it is going to be awesome. This startling reimagining of God of War deconstructs the core elements that defined the series-satisfying combat; breathtaking scale; and a powerful narrative-and fuses them anew.