Choose Production, Is there anyway to bypass it

While you do have to produce something, there are a couple of techs that give you alternative options to using your production on units, wonders, or buildings:

The technology Currency unlocks "Wealth" which converts a percentage of your city's production directly to gold. Similarly, Education allows you to produce research. These two options are typically below the wonders group in your production menu.

You can also change the focus of your city away from production (to food, commerce, etc) which will slow down your production, while providing alternative benefits to your civilization. Changing the improvements on your tiles can also shift the focus of a city from production to some other use - for instance, chopping down forests or demolishing a mine will reduce the production in a tile.