Is it possible to connect the dishwasher inlet to the existing copper pipes without souldering or needing a press tool?
Welcome to the Bunnings Workshop community @ema08. It's brilliant to have you join us, and many thanks for your question about installing a dishwasher hose.
A plumber can cut into that 15mm copper tube and install a compression tee. That tee has a 15mm female threaded outlet, so they'll need a 15 x 20mm nipple to convert it. They'll then be able to screw your 20mm dishwasher hose onto the tee. They won't need any specialised tools for this; it should only be a quick job.
On a side note, that flexible pipe is kinked too hard and needs to be replaced by a longer length. Not only is your water flow likely reduced, but it will burst at some stage in the future.
Please let me know if you have any questions.
Mitchell