Use the Ready action
The only way 5e offers to sort-of delay your turn is to use the Ready action:
Sometimes you want to get the jump on a foe or wait for a particular circumstance before you act. To do so, you can take the Ready action on your turn, which lets you act using your reaction before the start of your next turn.
First, you decide what perceivable circumstance will trigger your reaction. Then, you choose the action you will take in response to that trigger, or you choose to move up to your speed in response to it. Examples include "If the cultist steps on the trapdoor, I'll pull the lever that opens it," and "If the goblin steps next to me, I move away."
When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger. Remember that you can take only one reaction per round.
The Ready action only allows you to take one action or move your normal speed, so you cannot effectively use it to defer an entire turn (where you could do both). It doesn't let you use a bonus action, it requires you to use your reaction, and the action you take isn't technically on "your turn", so you don't benefit from any class features or abilities which state "on your turn" or have similar wording (though you get the benefit of abilities which are simply limited use "per turn"). Despite these drawbacks it's the closest you'll get to delaying your turn.
You can prepare your party to breach a door by having everyone who is before your point man in the initiative use the Ready action to declare what they'll do when the door is opened - useful examples might be like so:
- When Point Man opens the door and charges in, I'll move and follow alongside him (but I won't be able to attack until it's actually my turn)
- I nock an arrow to my bow and prepare to shoot whatever enemy is revealed when Point Man opens the door (but I can't move until it's my turn)
- As soon as the door opens, before the rest of the party rushes in, I'll cast Fireball into the far side of the room (but if we don't actually breach the door, my held spell is going to be wasted)
If you're not in a rush, you can probably have your point man wait a full turn while everyone readies actions, so that each ally will have a reaction to take when the door is opened. That's probably the best way to get the effect you want. If you're very lucky, and the enemy on the other side of the door was not expecting you, you should also get the benefit of a surprise round, where the party will get the benefit of all their readied actions plus a full turn before the enemy even has a chance to react.
If the enemies are aware you're there, however, they'll take their turns in the normal place in the initiative order, whether you've opened the door or not - so you should perhaps exercise caution, since an alerted enemy could just as easily Ready an action of their own to set an ambush upon the party when they open the door.