djdeth,
Working 
-heavy tiles
The speed of your build is determined by several factors, but in the early game the number of
is a cornerstone criteria, so 'yes' build mines and make sure that your citizens are actually working the mines - that is, in 'city view', ensure that there's a citizen (white circle) over the mine(s) or other
-heavy tiles, for example; Stone Quarries or Horse Pastures. In 'normal view' you can also see if the tiles are being worked due to the animations - small ore cars and flames coming out of Mines, Horses grazing within the Pasture, etc.
Perhaps worth also noting that Railroads over Mines and Lumbermills (and in some versions; Quarries) give a bonus
.
Specialist Engineers and Specialist Priests, and indeed 'generic' Specialists are also a souce of
. Specialist Priests (including merged Great Prophets) get a
bonus while the Angkor Wat wonder is 'active.
Secondly, some leader traits lend to faster builds for some improvements - for instance Industrious leaders get faster builds on Wonders and Forges, Spiritual leaders with Temples, and so forth.
Civics
Thirdly, your Civics can change the rate of production as well. Organised Religion sees a faster production rate for buildings if you've selected a State Religion and the city in question has that religion. Police State is another civic that gets fast builds - this time on units. The late-game State Property civic (via Communism) gives
to Workshops and Watermills, that while already productive by that time
-wise, are better at supporting themselves
-wise.
Fourthly, some builds get an accelerated production effect due to access to a resource. Faster builds on The Pyramids for instance if you have access to the Stone resource (you have built a Quarry on Stone within your borders and have built a road or have a river connecting the Stone to the city, or you have a trade deal with another nation that gives you access to the resource and the city in question is connected to your trade network).
+Productivity city improvements
Buildings such as Forges, Factories, Power Plants or The Three Gorges Dam, and the Ironworks improve productivity. Heroic Epic leads to faster unit builds in that city - as does a Military Academy if you've got Warlords.
Laboratories (depends on game version) and The Space Elevator provide faster builds for Spaceship Parts.
Merging some 
s into a city
Settling Great Engineers, Great Prophets, and/or Great Scientists in a city provide an additional source of
if you choose to do that.
Finally you can hurry productivity with tactics such as chopping Forests (as you have noted - typically more effective once you've acquired the Mathematics technology {depends on patch version}), as well as using the Slavery civic to whip the population converting citizens into
, and/or the Universal Suffrage civic to rush production with
.
You mentioned that you play on the same settings - so game speed isn't an issue here, but 'things' take longer to build on 'Epic' speed and 'Marathon' speed than 'Normal' or 'Quick' speed all other things being equal.
___________
I've probably missed something - but hopefully all this makes sense and is of help.
