MS SQL Server - Increase allocated memory
SQL Server will not use memory for buffer pool (its biggest use) until it needs to load pages from storage because they are referenced. Unless you are doing something odd to make memory allocation slow[†] then your delay is unlikely to be that but reading the data that it is being allocated in order to hold. I suspect that at the same time as those memory allocation waits, you have matching IO related waits.
To force SQL server to load things into memory, and therefore to allocate memory if available and needed, access things so that they need to be loaded. After starting your SQL instance, run a read-only workload so that your application's normal common working set is loaded into the buffer pool.
Don't just SELECT * FROM HugeTable as this is likely to load a bad balance of data (not the applications core working set) so the core working set will still need to be loaded from disk/network on next access anyway so you'll have the same IO delays. Also if HugeTable is truly huge SQL Server may see that it'll not all fit and not bother keeping a significant amount of it in memory anyway[‡].
[†] Running in a VM on an overloaded host so what looks like real RAM is really on-disk pages?!
[‡] Under normal circumstances you don't want an unexpected table/index scan on a large object to evict everything else from memory. A limit on how much is kept from one object for one query is an optimisation to try stop this from happening).