One thing you can do is have each enemy spawn point check the player’s distance from the point in each Update. Then, if the player is close enough, the spawn point spawns the enemy (or whatever you need it to do). This has the same effect as having a circular trigger area around the point (or a circular area around the player that activates the points), but if you’re only searching for one object (e.g. the player), then it’s simpler to do (and probably more efficient) than using physics triggers.
To get the distance between two GameObjects, have one, use Vector2.Distance(this.transform.position, otherObject.transform.position), or Vector3 if you need to workin 3D space.