Hi Op,
It's great that he has some ways of showing you what he needs, and a good start to use those times to reinforce words like 'drink' or 'coat' or 'playground.'
Good to get his hearing checked to rule that out. Good also to explain everything you've said here at the 2yo check and ask for support.
It would be good to learn some Makaton sign - reinforcing speech with a visual can help support him learning vocab. The easiest and cheapest way to do this is to watch Something Special on BBC iplayer!
There are games and activities you can do to encourage his speech development while waiting.
Make sure TV, radio, background noise is turned off when you are playing to encourage speech so distractions are minimised.
Get hold of some books that have lots of photos - of animals, babies, vehicles, whatever. Take time to look at the pictures with him and point and name each item. Reinforce the word with the Makaton sign if you can. Once you've pointed and named everything 'that's a cow... look at the pig oink oink... here's a sheep etc' you can ask him to show you something you've already named 'where's the pig? Show me the pig? Oh well done, can you say pig?' Give him waaaay longer than you think is necessary as a gap to answer - count to 10 slowly. That way if he's taking a long time to think about trying the word you don't accidentally cut him off.
Sing nursery rhymes repeatedly. With actions or signs. If he has a favourite, say twinkle twinkle little star, sing it several times and then leave out the word star to see if he will supply it for you.
A game to start developing his understanding of instructions:
Get a collection of animal toys or vehicle toys and name them in front of him - 'that's a tractor, that's a car, thats a plane.' Give the sign if you can. Then give him a simple instruction. 'Give me the plane'. You can get his dad or someone else to play first and demonstrate. Give him lots of praise if he gives you the right toy. Ask him to say its name too. Give him lots of praise for naming the toy verbally or with a sign and repeat it back to him. 'Well done! It's a plane!'
When he is doing well with these 'one word' instructions you can introduce another factor - multiple cars in different colours and ask for the red car, or a family of sheep and ask for the little sheep.
To get him to name his preferences, introduce choice between two items wherever possible. 'DS, choosing. Would you like milk or water? Milk or water?' You can support with PECS images here - little symbols for the item - where it's impractical to offer two glasses at once, but for clothes or shoes or toys I would probably just offer the actual item.
These are the sorts of things the SALT team are likely to ask you to do initially so if you've already been doing them you can move the process along a bit!