You can create a polygon (shape) which occupies exact physical dimensions. Do you want to digitize (draw) it yourself or do you have centroid/centre coordinates for the squares?
For this to work you'd need to have your map frame in a projected coordinate system.
Go to symbology and choose 'Proportional Symbols'
On the 'field' option just add an expression with the value of 0.5 (or you could add a new field and populate it with 'radius' values for the square then use that field).
'Data represents' - Radius (this is why we set to 0.5 not 1)
symbol form - square (options are limited here with symbol and styling)
@IB3 these are the steps:
1. Change your 2D symbol units to cm in Pro options
2. Set your point symbol to be a rectangle 1cm in size
3. Set a reference scale on your map of 1:100 scale
4. Set your layer to scale symbol when a refernce scale is set
Hey presto, you have a 1m square.
Obviously this also applies to any symbol. You can import your own SVG symbol instead.
Also useful: https://www.convertunits.com/from/meter/to/pt
Points don't divide nicely into metric units, but when you know the conversion, it's possible to set the reference scale such that 1 pt = 1 m. Where 1 m is roughly 2835 pts, a 1 pt symbol measures out to 1 m.