Yes, only if the Conservatives can't get a working majority and they can.
Basically, the party with the most seats usually gets the first opportunity to form a coalition or try to get a working majority. Only if that fails, then Labour will get a chance to form a government.
This BBC article explains this quite clearly:
Who gets the first go at putting together a deal?
The Conservatives, as the government in power before the general election, get the first attempt at forming an administration.
If it becomes clear that they cannot and Labour can, then Theresa May will be expected to resign. Mr Corbyn would then become the prime minister.
But the Labour leader does not have to wait until Mrs May has exhausted all her options before he starts trying to put a deal of his own together.
He can hold talks with potential partners at the same time as Mrs May. They may even be talking to the same people.
It's also worth mentioning that Labour doesn't seem willing to form coalitions with other parties at the moment and rather govern as a minority government.
Labour's shadow chancellor John McDonnell mentioned told the BBC:
“Therefore, although [Labour] don’t have a majority, which I deeply regret, forming a minority government is the best opportunity of a government that will be stable in the interests of the country.”
However, Labour's quite short of a simple majority in the House of Commons and that will lead to trouble when passing legislative and thus the government is unstable and unlikely to last long. But it isn't unprecedented as former Labour Prime Minister Ramsay MacDonald took office in 1923 even though Labour had lesser seats than the Conservatives.
Would that be sustainable?
Quite possibly not. Prime Minister Corbyn would be vulnerable to being brought down by a combination of Conservative and SNP votes. MacDonald’s government lasted only ten months before collapsing. Baldwin’s Conservatives won the October 1924 election handsomely.