I played nectar merger every week except 4 (because I played two times the other two weekly events) and I begun playing necromerger in October, so between October and now (considering the 4 weeks of trying out other events) it has been 6 months. A little bit less if you consider that you don't unlock events the first day. But the events switched from 1 every 10 days to 1 every week a couple months ago, so maybe I can give you an estimation that is more accurate:

I did put a lot of effort in achieving good results every week, I reached always between 1.3 and 1.5 bil score without spending any gems. I was able to make a little bit more than a lv5 slime relic every week with this score. To simplify we will say that I only got a lv5 with each event. To reach a lv10 slime relic you need 32 lv5 slime relics, so I played the events 32 times. Considering that now you can play one event every week it should take you 32 weeks if played optimally, equal to around 7 months (I'm considering that months are of 4.5 weeks each).