Great helms did exist in this era and for another decade or two (Henry V of England had a beautiful one) but they had no place on the battlefield anymore and were strictly used in sport jousting. In 1403 they 100% would not be worn by soldiers.
The steel mastery helmet above is based on an Italian carving from the 1340’s and so is in armour terms at least 3 of generations of fighting man removed from the era of the game. It’s too old a style and would, like the greathelm, no longer be worn by soldiers on the battle field in 1403.
Bascinets are the major helmet of this era and probably 75% of all helmets worn by professional fighting men in this time frame would have worn one. Within the era that Bascinets were common place (approx 1340 to 1430 as a very rough time frame) the shape and style changed usually and we should be careful which ones are modeled. At the end of the 14th and into the early 15th century the most common European style was the one with the high swept back point rather than the more rounded sort. In eastern Europe the ‘onion top’ style was still being used as an interesting local type. The visor would have almost universally been a variation of the houndskull style and would be mounted to the SIDES of the helm and not in the old fashioned central ‘Klappvisor’ style. A maille aventail would be attached all around and sit up as high as the bottom lip at the front and at this time a neck guard could being to be attached as the bascinet starts to evolve towards the grandbascinet style with it’s solid next protection. The correct style of bascinet was the fighting helm of this era and that should be represented in the game.
Other styles are of helm did exist but were less common and therefor harder to typify. Several styles of wide brimmed ‘kettle helms’ are shown frequently including one which is has the same skull profile as the bascinet above but with a wide brim which sweeps out to a point at the front (there’s a beautiful surviving example in paris). Helmets worn by the lowest ranks were the most varied with everything from disks or square lames attached to a felt or leather cap beneath to simple iron or steel domed caps worn with padding under it.
Fashions were a major part of armour for all but the lowest ranks and armour styles evolved constantly with distinct styles appearing almost decade by decade. If the game can find a way to reflect this accurately it will really help to set it in 1403 and help create the immersion I hope they achieve!