There actually are a few points we can look at, and one large turning point in the history of Games Workshop as a company that led to their continued rise. That was the critical mass of the Warhammer 40k IP going from brand new to taking off in the mid 90's, and the buyout of original GW owners Steve Jackson and Ian Livingston by a group led my manager at the time Tom Kirby. Kirby would become and Chairman of the board in one form or another from then until his retirement in 2017, he shaped much of what GW did for better or worse over that tenure, but undeniably saw a company that was still growing but one of several, and tacked hard towards the tabletop miniatures side and saw explosive growth. And even today the self identity of a model making company first and foremost that also publishes rules for them remains.

It really comes down to that they were really the first company to make the jump hard from small scale model and rule making in the vein of Dungeons and Dragons and other role playing rule sets, which they published and were even the DnD distributor for the UK early in company history. But also not the historical focused large scale miniatures battle rule sets, Gary Gygax had even created a medieval focused rule set early in his career! From the earliest days of hobby tabletop gaming in the late 1800's, to HG Wells and Little Wars to post WW2 products, it was by and large historical, or for the time 'modern war' focused, while more modern games like Bolt Action, Flames of War, and Team Yankee continue this tradition it is still for those looking for something more imaginative or open narrative, something limited.

So while Warhammer Fantasy Battles may not have brought a ton new, at least to start, it still was steeped in tropes familiar to most of its market, and was a gaming space that a company producing high quality, customizable, and still affordable game for could do well. With early versions of Warhammer Fantasy premiering in the mid 80's it started gaining popularity, but the Sci-Fi side was still mostly just dabbling with products like Rogue Trader. But With 1993's 40k 2nd Edition, and 4th Ed of WFB shortly after the direction of the company was set. Comparatively high quality sets(which of course were highlighted whenever possible in high gloss color in places like their White Dwarf magazine), with rule sets designed for predictability in performance, and while parts could be ignored, would also help impose some order in style of play, and of course encourage purchase of a variety of sets from the range to create a full, legal, balanced army. The 90's also saw the arrival of staff members like Andy Chambers and Gavin Thorpe who would dominate much of the rules writing and even lore development for both sides of the business for years to come, and who worked with Rick Priestly who had written the original Rogue Trader proto-40k rules from then on.

That isnt to say GW didnt face competitors, notably two ex employees launched Fantasy Warlord in 1990, but it was never a success.

So by 1999 GW had two expansive ranges with well developed rulesets, and for better or worse had spent most a decade understanding their role as being one to sell models first and get people then to play the game to buy more models from there. It of course would not stop there, as you note the ubiquitous of Warhammer has only really grown(though now it is mostly 40k and Fantasy Battles has now been ended as a rule system and reworked into Age of Sigmar) but it was a +30 year process which really wasnt taken seriously or designed around a core expansionary business plan for the first 5.

Another point actually that should be mentioned re visibility: GW was very good at expanding their IP coherently. There are two other tabletop IPs that have had significant growth and wider recognition that is comparable to 40K. Battletech and D&D. Other wargames and RPGs have had novel lines and computer games, but those are by far the biggest.

D&D is an RPG, and people know that. If you tell people you roleplay, they'll think of D&D - even though the company did and does other stuff. And they had D&D somewhere on pretty much everything they did.

Battletech, meanwhile, has had huge computer success and had some very popular novel lines - but almost all Battletech computer games never mentioned the word Battletech, and weren't really adaptations of the game or anything close to the game (I got into it because of Mechwarrior 2, for example). Tell people about Battletech, they're not sure what you mean. Tell people about Mechwarrior (or even Mechcommander), and they know about the computer games from the 90s.

In 1999, people knew about BT as well as GW lines. Heck, it had a TV series. It's just that BT has done REALLY badly since on the tabletop, even though it still has a surprising amount of brand recognition when you pull together all its various imprints.

So that's the other thing that helped 40k be ubiquitous - the other big tabletop wargaming brand that had anything like the same popularity or exposure went and imploded.