On what date do the events of the Lost Mine of Phandelver adventure happen?

I bought the D&D 5e Starter Set a few weeks ago, and I’m beginning to think about how to drive the scenario as I’ve already read it and I’m at the stage to get familiar with the rules.

Yesterday I created my first character sheet with one of my future players (we’re not going to use pre-generated sheets) and we talked about his character’s lore and background – he will be playing a nobleman, a prince).

I thought that there could be a king in Neverwinter (the closest bigger city to the location of the adventure) , so we could link his background to the scenario. Again, his character would be the son of a king, who, after finishing his Paladin training, wants to go an on an adventure to gain experience and prove his value and that he is adequately trained to potentially govern one day.

However, when I searched for Neverwinter lore, I found out that while there were indeed kings, they didn’t exist towards the end of the timeline.

Given that, I tried to find out at which date the events of LMOP take place, but I didn’t manage to find it anywhere in the books.

So, based on already existing modules or deductions based on facts in existing modules, when do the events of LMOP take place?

If the date is deducted instead of directly stated somewhere, you have to support your answer with official sources, not just a more or less educated guess. The better the answer is supported by sources, the better.