I believe within the first week of playing, you get 2 emails that each offer 50 diamonds, one is to verify your email, the other one I forget.
Otherwise, sadly, there's other way to get diamonds.
If you don't want to spend money, progression will be slower, which is to be expected.
Best bet IMO is to wait until you get a diamond sale(they happen fairly often, 10-100% more diamonds when you buy.)
Without and sales or deals, getting all 5 builders takes roughly $30, but if you plan on playing a while, it's well worth the investment.
Again though, spending money isn't a requirement, but it's more so to bring you some QoL features.