Frames are designed around forks with a particular axle-to-crown dimension, which in the case of suspension forks correlates pretty closely to travel. So it's not just a question of suspension fork or not; it's a question of what the axle-to-crown should be, or how much travel. For example, very early suspension forks with 60-70mm travel didn't require a radical change in geometry from the fully rigid mountain bikes of the day, and could be plugged into them and yield something reasonable.

To the question of how to know what you're dealing with or what to do in the case of a bare frame with no information obtainable as to what it is:

This sounds geekier and more complex than it is, but the best approach is to take all the point-to-point distance and tube-to-tube angle measurements you can from the bare frame, use those numbers to model the frame either on paper or in a simple 2d CAD program (freeware is fine), and then go from there to see what different fork axle-to-crown lengths are going to get you when you plug them in. In CAD this just means you'll be making the model of the frame, then rotating it around the axis of the rear axle as you stick in lines of different lengths to represent the different forks.

You'll then be able to take one of two approaches. If you want to try to figure out the best guess you can as to what the bike came with originally, you can plug in different axle-to-crown lengths until you find one that gets you head tube and seat tube angles (which change with fork length) that both look suspiciously close to cleanly rounded numbers, say 71 degrees up front and 73 in back for a lot of hardtails. Manufacturers tend to design things in a way where if you measure the built bike, those angle numbers are similarly clean. There's not all that many length/travel groupings of forks to work through.

Alternatively, once you have your paper or CAD model, you can just plug in different axle to crown numbers until you get one that results in head tube and seat tube angle numbers that make the bike how you want it, or as a way of getting the longest travel you can that still keeps them within your own metric of what's reasonable. BB height also gets affected.

When making the model, remember to include headset stack height as applicable (14mm of lower stack height for an external cup headset, 3mm for ZS, and 1mm for integrated are the numbers I'd use).

Frames are designed around forks with a particular axle-to-crown dimension, which in the case of suspension forks correlates pretty closely to travel. So it's not just a question of suspension fork or not; it's a question of what the axle-to-crown should be, or how much travel. For example, very early suspension forks with 60-70mm travel didn't require a radical change in geometry from the fully rigid mountain bikes of the day, and could be plugged into them and yield something reasonable.

To the question of how to know what you're dealing with or what to do in the case of a bare frame with no information obtainable as to what it is:

This sounds geekier and more complex than it is, but the best approach is to take all the point-to-point distance and tube-to-tube angle measurements you can from the bare frame, use those numbers to model the frame either on paper or in a simple 2d CAD program (freeware is fine), and then go from there to see what different fork axle-to-crown lengths are going to get you when you plug them in. In CAD this just means you'll be making the model of the frame, then rotating it around the axis of the rear axle as you stick in lines of different lengths to represent the different forks.

You'll then be able to take one of two approaches. If you want to try to figure out the best guess you can as to what the bike came with originally, you can plug in different axle-to-crown lengths until you find one that gets you head tube and seat tube angles (which change with fork length) that both look suspiciously close to cleanly rounded numbers, say 71 degrees up front and 73 in back for a lot of hardtails. Manufacturers tend to design things in a way where if you measure the built bike, those angle numbers are similarly clean. There's not all that many length/travel groupings of forks to work through.

Alternatively, once you have your paper or CAD model, you can just plug in different axle to crown numbers until you get one that results in head tube and seat tube angle numbers that make the bike how you want it, or as a way of getting the longest travel you can that still keeps them within your own metric of what's reasonable, or as a way of figuring out how to work with what you have, etc. BB height, standover, and minimum handlebar height also get affected.

When making the model, remember to include headset stack height as applicable (14mm of lower stack height for an external cup headset, 3mm for ZS, and 1mm for integrated are the numbers I'd use).