It really does depend on the phone ... Cisco Linksys SPA phones can have their 'Interdigit Short Timer:' settings reduced so that the phone will just dial-out after a few seconds. Yealink phones are able to be configured to 'see' 'Dial now' rules that let the phone dial at the completion of a sequence [e.g. 0xxxxxxxxxx tells the phone to dial-out immediately at the completion of an 11 digit UK dial-string].
You might also find that the phone will work best if the user 'pre-dials' ... i.e. they key in the number they want to call, and then pick up the handset. Going off-hook usually initiates dialing.
Best regards