“Theme-first or mechanics-first” might be the most asked “big question” in the board game community. It’s a bit of silly question. The false dichotomy we use to discuss these two elements, however, is really useful.
Theme and mechanics are inseparable parts of board games as a whole. When people talk about mechanics, they tend to mean to strategy, tactics, and rules. When people talk about theme, they tend to mean narrative, feelings, and the intangible aspects of a game. It’s a left brain / right brain mindset. The theme is how a game feels and the mechanics are why the game feels that way.
There is no hard-and-fast line that splits mechanics and theme. They’re two opposite ends of a continuing spectrum of detail.
Now that we’ve accepted that theme and mechanics are imaginary, abstract concepts, let’s put them to use. Start with feelings first, then think of ways that you can convey those feelings. It’s easiest to think of theme first – “it’s going to be a scifi, zero-sum game set in crapsack corporate dystopia.” Then you can get more specific about how to symbolically represent that theme – “the objective is to be the sole survivor by cutting your opponents down to size.” Then you can start developing mechanics. The further you go, the grittier rules become. Through playtesting, you can answer the question “do the mechanics suit the theme?”
Once you’ve got mechanics to suit a core theme, you can develop the theme a little more through art, story, and graphic design. At this point, you can start developing marketing around the theme. Game design starts with theme and ends with theme, but most of the time is spent in mechanics.
Theme and mechanics are interwoven at the fundamental level. They’re not concrete things, but rather viewpoints. Theme is what your game looks like from 10,000 feet up in the air and mechanics are what your game looks like under a microscope. Mechanics are atoms and the theme is an organism. Figure out the theme you want to capture, try building it through mechanics, then playtest and tweak until you successfully captured your desired theme.