I agree that no matter what software you use, there will be some masking involved and a change to the background. OK guys, are you gonna tell me to use Topaz filters here?!! Anyway, you are talking about Photoshop, so I will stick with PS and native tools and solutions. There are of course always multiple ways to do anything in Photoshop, so you're likely to get more opinions, a good thing as one method may work better for you than another.
First of all: IMO, there is simply no way to add depth of field to a pure, flat color field. You will need to add a new background or make changes such as adding a gradient to the white, which may create an inverse illusion of depth, unless you mask out the kids.
Depending on how perfect you want your selection of the children to be (ie: without white halos - white around the edges), or whether the background immediately around it will remain white, will affect your choice of how to do this.
The best solution of course, would be in the photo shoot, placing your subjects in a different environment to begin with and adjust depth of field with camera settings. But . . . post processing . . .
1) A very quick solution, but probably the reverse of what you really want, would be to create an elliptical selection around the kids, invert the selection, create a new layer above, and add a radial gradient. As I said, this may create the opposite illusion, pushing the baby forward instead of the BG back.
2) On to creating a selection instead.
The best selection tool is usually the pen tool with refine mask to restore some soft, fringe hairs. But the pen takes some learning and experience, a fair learning curve actually.
Since your BG is white, you can quickly select it with the magic wand or quick select tool. Then zoom close to the edges and adjust the selection to the edges. Invert the selection (if you select inside the baby instead of the white, you won't invert) and add a layer mask.
Refine the mask, choose a black BG so you can see white edges. I suggest: if you need to replace a bit of hair, check smart radius, keep it small to begin with, and run the circle over places where hairs should be, but don't run it back and forth or you'll pick up more BG. Add a little bit of smooth edges, not too much or it will look feathered and blurry. I don't recommend feathering on these borders. If there is a lot of white still, consider using the edge refinement and adjusting it to the negative. You'll get a preview, so you can go positive and negative and see the results.
Finally, you can go back into the mask and fine tune any edges, using the brush to paint with black to remove background or white to restore the image or BG.
Now you can add any background you like. If you want to keep the entire background one color, you can use gradients to do that.