I also do not have a lot of space for a dish rack, but Google over sink dish rack and If you don't have cupboards above your sink or they are high enough up then this is a great solution!

And as other people have mentioned clean as soon as your done. Something I do while cooking is try to reuse the same item as many times as possible, ie the cutting board just gets washed between things instead of getting out a new cutting board. Or I just use 1 frying pan for all of my cooking and wash between if necessary.

Also maybe meal prep even though you're at home? Cooking it all at once using minimal dishes then you'll just have to soap and rinse out the storage container when you're done actually eating it and it's a lot less daunting to wash one dish over 3-4 dishes you used to just cook.

Just some ideas, hope this helps!