Michael Burnham was the farthest thing from a future Starfleet Captain in Star Trek: Discovery season 1. When Michael was released from prison and brought aboard the USS Discovery by Captain Gabriel Lorca (Jason Isaacs), she was assigned as an unranked Specialist. The lowest on Discovery's totem pole, Burnham began her climb back to becoming a Commander. More importantly, Michael claimed the highest principles of Starfleet. Still, a part of Burnham doubted a Captaincy was in her future, but Emperor Burnham always knew better.
Emperor Georgiou Always Knew Michael Burnham Would Become Star Trek: Discovery’s Captain
"Captain Michael Burnham" Already Existed In The Mirror Universe
When the USS Discovery jumped to the Mirror Universe in Star Trek: Discovery season 1, the revelation that the alternate reality's Philippa Georgiou was the Terran Emperor was a shock. However, just as eyebrow-raising was Georgiou calling Specialist Michael Burnham "Captain Michael Burnham." At first, the Emperor thought Michael was her adopted daughter, as the Mirror Universe's Burnham was Captain of the USS Shenzou. Yet this was a clue towards Burnham's future in Star Trek: Discovery.

Georgiou's prediction came true.
After saving the Federation from Osyraa (Janet Kidder) and the Emerald Chain, and learning the cause of The Burn, Michael Burnham was promoted to Captain of the USS Discovery. Georgiou's prediction came true.
Georgiou Is Star Trek: Discovery’s Strongest Hint Toward Burnham’s Destiny As Captain
Emperor Georgiou Always Knew What Michael Burnham Would Become
The Guardian of Forever sent Emperor Georgiou to the early 24th century, as seen in Star Trek: Section 31.
Having raised the Mirror Universe's version of Michael Burnham, Emperor Georgiou had a unique insight into the heroic Michael of Star Trek's Prime Universe. In hindsight, Emperor Georgiou knew that commanding a starship was Burnham's first, best destiny, and Philippa did her part for Michael to fulfill it. Although Emperor Georgiou never gets to see Captain Michael Burnham come to fruition, the seeds were there step-by-step in Star Trek: Discovery's first three seasons.