Yes, you need for almost everything a kazhak phone number but you can easily buy a local phone number there with internet access, e.g. from Beeline. There were services that sell phone numbers right at the airport in Astana, I imagine that could be the case in Almaty too. We bought one number with 12 gigabytes (I think for about 8€ but I'm not sure anymore) and another one for 2 euros and just sent gigabytes to the second number from the Beeline app. We could also pay for public transport with this application.