Our sinks were built in, but their cabinets were low and bending hurt my back. I determined the cabinets could be raised by adding a horizontal board just above the place at bottom that is indented for your toes. It added about five inches, bringing the counters up to the height of our kitchen counters. The board was stained to match the cabinet and is right under where the cabinet doors open. The line of the board is hidden by a length of wood trim. This raising up did require adding pipe to the water lines under the sinks to fill the pipe gap; moving the very large mirrors (no breaks or chips!) upward and moving the lighting above the mirrors up, as well. Took one day of work by carpenter and helper. Well worth the cost.

In short no you can’t or shouldn’t. Undermounted sinks aren’t only suitable for solid worktops such as granite, quartz, solid timber and solid surface. Laminate worktops are not waterproof and they will blow so you’ll end up ruining your worktop. Can’t see in detail from the image exactly what it is.

https://ebay.us/m/WYbPO4 You need a deck filler like this and two taps heads

You could consider an insurance claim. Ideally to fit the new worktop the splashbacks need to be removed, this will probably damage the walls so its quite a big job. You may find a fitter who is prepared to work with the splashbacks in place, but the sink run would have to be cut short to fit in between the splashbacks and then the gap filled with silicon. How to get the worktop in position may also mean removing some wall units as well. then for the 2 side worktops being able to slide under the splashback and making a decent job of the masons mitre, keeping an even overhang to the doors etc, not a job i would of undertaken when i was fitting. You mention water resistant laminate, if you mean compact laminate, the max thickness is 20mm so there'll be a gap. If you mean laminate but made with 'green' chipboard, it still needs sealing and if its constantly subjected to moisture it will still blow. I'd suggest a new worktop in a stone/abstact pattern colour as you have a modern door style, make sure it's a bullnose and not these edged worktops [i've seen these fail around sink area], get rid of the splashbacks and fit some metro tiles in a brick pattern, also get rid of the windowsill so that is also tiled instead of that gap you have under the sill. Reason for tiling is that if the splashbacks have been stuck on with silicon, even if the wall isn't damaged any silicon may affect the new paint. For the sink, you mention that you want to wash oven trays, so for a bigger bowl opt for a single bowl with a right hand draining board as well, looks like its a 600 sink base in the pics so there's plenty of choice, personnally i'd have a 1.5 bowl though as Betty says, also opt for a composite/granite [as below] so you can just drop the sink in place on a bed of silicon beading, stainless steel would ideally need the clips underneath [there are a few push in stainless sinks though with spring clips].