Its definately worth being very persistant with getting a dummy accepted. 12 weeks is late, but not too late to establish one I don't think.
The spitting out is a baby reflex reaction (called the Tongue Thrust) that all babies have and most have lost by 6 months old. Many lose this reflex much easier and earlier than others, indeed bottle feeders often have to overcome very quickly.
So the spitting out of the dummy is not distaste, it doesn't mean baby doesn't like it. It's just that a reflex reaction in babies will be to push forward (spit out) any foreign object in their mouth. It saves newborns from choking.
Enough dogged persistence can overcome it. By that I mean literally try all the time, every single day. Try when hungry, when not, when tired, when not, when asleep, when nearly asleep, when playing, when happy, when grumpy, given by other people, give in different position, given immediately after breastfeeds... any any other opportunity and situation you can think of.
I know that sounds like a massive amount of hassle and I know lots would say, why on earth bother? But then the dumny absolutely AMAZING in my view.
It is the single most important tool for no crying independant (ie not on you) sleep.
I basically think any other no crying method wok involve embracing feeding to sleep and/or cosleeping. Or any other route to independant sleep will involve crying and distress, to varying degrees. Whereas the dummy is the simplest and easiest of the no-crying independant sleep solutions.
So when I had a dummy refuser, because this was DC4 and I had a full appreciation of the value of the dummy, I was utterly and completely persistant about it.
Much like if you had a bottle refuser who was losing weight and must accept a bottle even though they don't want to, I would approach a dummy with the same level of certainty. I would literally keep going, with increasing persistence, until my child took a dummy no matter how long that took. In the event it took 7 weeks of daily, all of the time at every opportunity, persistence to get it accepted. But not, was it worth it.
Anyhoo, all my waffling aside, my recommendation is to consider if you could be more persistant with dummy use. The longer you leave it the harder it will be though.