It might be possible to create a DoT at the time of purchase that gives your partner 50%. The only problem is that it might be against the terms of your mortgage and therefore your solicitors might refuse to do it. But if you do make it 50/50 via a DoT then the change to joint names doesn't involve any transfer of equity (even though that's what the mortgage company will call it) and so there is no SDLT.
Technically, if you do create a DoT then I believe there is a requirement to attach a form A restriction. (and I believe there is some date in the not too distant future where you will have to register the DoT with HMRC if you haven't already converted to joint names)
Another possibility might be to explicitly document in a letter to your partner that the property is owned 50/50 from the date of purchase. I'm not 100% sure that a letter is allowed to document land and property.
Unfortunately, this is one of those problems that has both legal and tax effects and your solicitors won't advise on the tax side and an accountant won't advise on the legal side. I'd first suggest talking to your solicitors as to how you can achieve a 50/50 beneficial ownership from purchase.
The other thing to be aware of is that if your partner owns part of the property then I think the higher rate of SDLT will be due and it's not 100% obvious to me that it is reclaimable when your partner sells their property because there's no single transaction that triggers a reclaim. SDLTgeek might know better if he sees this.
How much is the mortgage for? if it's less than 250K then I don't think you need to worry about SDLT on the transfer of equity anyway as your partner will only take on 50% of the debt when the transfer happens.