What you could do is creating the texture object (new BABYLON.Texture(...)) at start with an empty texture and only update the texture data later on when you have loaded the file. You could even create a RGBA texture instead of a regular texture, as it could be easier to update. See how @billchen0412 has done it here:
https://playground.babylonjs.com/#YDO1F#664
The only difference is that you would not get the pixel data from readPixels but from loading the texture file instead.