I'm just an ACCA student and working with customers' accounts, invoices, credits as a second hand for our finance team, advising our customers about the payments and transactions on a daily basis. I'm not a professional, nor an accountant.
Best to issue a non VAT invoice or wait until the VAT registration process is done and then start issuing sales VAT invoices. You may arrange an agreement with the clients that VAT invoices would be issued, let say, after a month (if your application process has already started). However, that's not the best option (leaves you with a cashflow delay as it pushes the payment terms). VAT applications can sometimes be lengthy and early applications are always recommended. Depending on sales amounts, issuing a non VAT invoice but later getting a VAT reg backdated isn't a big deal. You may decide to issue a credit note and reissue a VAT invoice (shouldn't be backdated, but some businesses do that and I'm not entirely sure if that's legal. It depends on your relationship with client and the length of the period of a backdate between the actual date). Generally, invoices can be issued when good/services sold/provided or agreement/contract signed, or money for goods/services received. So, if a client pay you for a non VAT invoice, you issue a credit note with an actual date when you receive you VAT number, then issue a VAT invoice with an actual date and return the customer a credit, if they don't pay VAT.
Just out of curiosity, are you a new business, or existing which overlooked reaching (or maybe even overdue) VAT thresholds, or it's something to do with market change and a need of VAT (eg., changes in market due to Brexit).
Claiming VAT with expenses - the situation is similar. If you are not 100% guaranteed and don't have any written proof that it's going to be backdated (and to which date), then best is whether hold with VAT expenses. However, that's not always possible. Then safest way is to not claim VAT expenses for the invoices prior your VAT issue date. Depending on the nature of business, you may loose very little or very much.
I unfortunately don't know the actual practise in Ireland regarding as Irish tend to create their own "practical exceptions" just because there was a hope everything will be fine. But that's just me being precautions. I don't think Revenue would be lenient if something isn't aligning withing the dates.
Again, I'm not an accountant, all the above is my personal opinion, based on what I've seen, heard or is my interpretation and understanding with a limited knowledge in accounting.