On a tangential matter, I disagree with avoiding opportunities for teaching children delayed gratification in such a high impact way.
Think about it this way: every time you rightfully don't give your child something they want due to their bad behavior, you're giving them an effective lesson and improving their future life.
It's cruel to intentionally create situations that trigger a child; it should happen organically. It doesn't take long for children to adapt to understanding they won't get their way and start adopting appropriate self control.
Especially with modern research showing the damaging effects of corporal punishment, parents should take opportunities when they arise to discipline their children in a way that is meaningful to the child: withholding a toy they desire or another form of leverage.
My comment on 2-3 days? That’s too long for a child to make the connection between behaviour and outcome. I love delayed gratification and would ask that we wait to play with the new toy until after we get home, eat, tidy up, etc. I hope that they make the link between waiting, being praised for doing a good job with something else, then playing.
Did you know? The 2-year-old will tantrum regardless where you are, and buying online means you don't have a quick out on hand (either getting the toy almost immediately after calming down and ensuring enough separation between the tantrum and getting the toy, or some stopgap alternative toy that's a tenth of the price).