You don't, you only need the ship model when placing it on the board initially. In cases like this, simply interpreting the rules literally keeps things easy: 'Pay for that Dreadnought by taking
a Build action and spending the Materials.'
This came up at the world championships. Literal reading of the rules do not require you to have the ship model to complete the action. You simply take a build action and spend the materials.
A logical analysis of the action would conclude that this is a build action but split between two different turns. The part of the build action that required the model be placed on the board was already satisfied 2-3 turns ago when you played the distortion tile and placed an available ship model on the board.