When rendering, my image has an acceptable resolution at a very quick stage – when sampling is at about 100-200 / 4096.
Where could I set up blender, so it continues on to the next frame when it reaches that sampling point?
Either you turn off the noise threshold and specify a set sample count (100) for rendering (render properties, sampling panel), or you turn on the noise threshold and you adjust the value so that the quality seems sufficient to you. For reference, I use a threshold of .005 for rendering
You can enter the desired value in the rendering sample settings.
