It appears so
Nothing in the description of the magic item specifies an expiration to this increase. Your Hit Point Maximum will be set to the higher amount, and any further increases will not reset the improvement.
That being said, having access to a rare magic item at level 1 is fairly unlikely, and this is much less effective at higher levels when you start getting access to rare magic items.
Instead, his clause is likely intended to be useful for when a hit point maximum is reduced by certain kinds of undead, such as a mummy:
The cursed target can’t regain hit points, and its hit point maximum decreases by 10 (3d6) for every 24 hours that elapse.
… in these cases, greater restoration is the best way to get back to normal since it can end:
One effect reducing the target’s hit point maximum