To the palpable disappointment of her critics, it didn't work out like that.
Instead, Ms Sturgeon will today overtake Mr Salmond, her one-time mentor, as Scotland's longest-serving First Minister, reaching 2,743 days in office.
It is a remarkable achievement, and perhaps all the more so given the unprecedented strains of the past few years.
But what has she done with that time and what might her legacy be?
Those close to Ms Sturgeon point to policies such as the expansion of funded early learning and childcare.
This has almost doubled to 1,140 hours a year under her leadership.
They also highlight the roll-out of devolved benefits and the creation of Social Security Scotland, as well as measures to tackle child poverty, such as the Scottish Child Payment, which will increase to £25 a week by the end of this year.
Elsewhere, climate change is seen as a key issue.
"There's just no two ways about it – Scotland is at the absolute bleeding-edge of what any country in the world has done," one insider said.
Of course, opposition parties see things very differently. For them, Ms Sturgeon’s time in charge has been marked by incompetence, secrecy and a paucity of ambition.
“Never in the history of devolution has there been a First Minister with so much power and time, but who has done so little with it,” said Scottish Labour leader Anas Sarwar.
Scottish Tory leader Douglas Ross insisted Ms Sturgeon’s story is one of “failure and broken promises”.
But even her worst critics concede Ms Sturgeon is a consummate politician, adept at playing the game and turning situations to her advantage.
Her enduring popularity with voters is a source of frustration for the opposition. Labour sees it as a wasted opportunity.
"If all you cared about was a popularity contest, we would put Anas Sarwar on Britain's Got Talent and have him play the spoons," one party figure said.
In truth, Ms Sturgeon’s record is mixed.
She staked her reputation on education, with the SNP pledging to “substantially eliminate” the attainment gap between rich and poor school pupils by 2026.
But last year a joint report by the Auditor General and the Accounts Commission found progress had been limited.
The gap remains wide and the pandemic has exacerbated existing inequalities. That 2026 pledge looks unlikely to be fulfilled.
Drug deaths are by far the worst in Europe and have risen sharply under Ms Sturgeon’s watch.
Action is now being taken to turn things around, but for many it is too late.
The First Minister previously admitted her Government took its eye off the ball.
Meanwhile, the health service does not have its troubles to seek and the CalMac ferries fiasco has proved an enduring transport headache, which ScotRail may yet worsen.
The charge of secrecy is also justified, although this often goes hand-in-hand with power.
At the same time, there have been successes, such as the childcare expansion and the launch of new benefits, and few would dispute Ms Sturgeon’s skill as a communicator.
This came to the fore during the pandemic, when – to her credit – the First Minister held press conferences on an almost daily basis.
It was an exhausting time to be a journalist, let alone in charge of a Government.
Serious questions remain over the decisions taken during this time, such as moving hospital patients into care homes, and the coming Covid inquiry could well prove damaging.
But Ms Sturgeon’s ability to connect with people and communicate calmly and clearly was an undoubted asset.
It is perhaps unfair to assess the legacy of a politician who is still in office, and insiders claim Ms Sturgeon is going nowhere fast.
"This isn't someone winding up and looking to polish her legacy,” one said. “This is someone with stuff to do.
"Frankly, it's someone who feels like they've lost a couple of years to Covid.”
Coming plans to create a National Care Service, billed as the biggest public sector reform since the birth of the NHS, are certainly ambitious and will take years to implement.
Meanwhile, the cost-of-living crisis will only become more pressing in the months ahead. Will it necessitate some radical and innovative interventions?
Genuine action on climate change also offers plenty of legacy-building potential.
But as so often in Scottish politics, the constitution towers over everything.
Ms Sturgeon leads a party that exists to advance the cause of independence. It is the glue that holds it together.
She insists she wants a referendum to be held next year, but very few believe this will happen. In fact, the prospect feels increasingly ridiculous.
Major questions remain unanswered and time is tight.
Scotland is stuck, its politics dominated and defined by the Yes/No split. There is an unhealthy sense of political stalemate and an inability to move forward.
If the UK Government keeps refusing to play ball, it is hard to see where Ms Sturgeon goes next.
The sneaking suspicion is nowhere, really – even if there are some entertaining diversions into the courts along the way.
Scotland came closer to independence than many thought possible under Mr Salmond.
If Ms Sturgeon fails to move the dial in any meaningful way, there is a risk that will come to define her legacy just as much as anything else.