If you don't have a French press, you can shake the cold foam ingredients together in a cocktail shaker or a jar with a tight lid but it'll take a little bit more work.
The vanilla syrup and cold brew coffee can both be made ahead of time. The cold foam is best when it's made right before assembling the drink.
Use store-bought or homemade vanilla syrup. Homemade is pretty quick and easy to make, so give that a try!