I personally believe in Having or Using Multiple Strategies to Grow an Account,Having Multiple Ways to Grow an Account will speed up the Growth like never before but all you will be limited by is How much Can you Invest into your Page:
1.Viral Content - Viral Content is an easy way to grow and make a page viral within days.It's very easy to find a Viral Content,You just need to watch upon what's going viral on your Explore Page,Watch for the Most Recieved Engagement Posts on your Competitor Accounts,You can even use tools for Finding Viral Posts but presently I do not know any.
2.Manual Interactions - The Best and the Most Safest and Organic way to grow your Account if you know how to be as Random as Possible and with Following the Daily limits.
You can do around 120-150 Follows,150-250 Likes and 25-40 Comments a Day and if you interact with your target Audience Consistently on a Daily Basis,it is definately going to help you somewhat as you still can reach around 350-500 Individuals in a Day with different actions.
3.Mother Slave Method - Works Gold if you can keep your Accounts Stable.Creativity decided how well your Mother Slave Setup be Beneficial for the Mother Account.Believing in Quality Slaves which can give you 50-100 a day instead of Bulk Spammy Slaves which can give you 50-100 a day is much much better,You just need to think about Quality and Being Creative with this Method.