Is there a way to identify number of wallets opened by an exchange
You won't be able to see the number of wallets, but you could get quite an idea by looking at the number of adresses an exchange generated.

( Exchanges such as poloniex only have 1 wallet for all their customers. )

See https://www.walletexplorer.com/wallet/Poloniex.com/addresses

I'm not entirely sure if walletexplorer also tracks coinbase adresses, but in the case it doesn't, you can use http://matbea.net

They currently track over (28.500.000+) coinbase adresses.

https://blockonomi.com/matbea-trace-bitcoin-address/

^^ (I wouldn't recommend using their webwallet though, and i'm also not saying that this is 100% indexing all adresses.)

For example, using matbea.net, i was able to identify 1DUiLkf34q7MVxtRkMAXVtP42UNGRrbftY  as a coinbase adress.

https://www.walletexplorer.com/wallet/000001e522b362b7?from_address=1DUiLkf34q7MVxtRkMAXVtP42UNGRrbftY