Yes. Fidel Castro was nominated by a Municipal Assembly in the City of Santiago de Cuba as one of several delegates to the National Assembly from Constituency No. 7 in that city. Unlike elections that we are familiar with, only one candidate is nominated for each seat in the National Assembly. Voters, by means of a secret ballot, will accept or reject that candidate. If the candidate is rejected by the majority, another candidate must be put forward by the Municipal Assembly, and another vote held soon afterwards. Fidel won his seat in the National Assembly with 99% of the vote. (All of the other candidates in his Constituency won their seats as well.)
The 601-member National Assembly elected him President of the Council of State, the Cuban head of state, by the following process: Nominations for this position (and others) were submitted anonymously by members of the Assembly. For this particular position, the member with the most nominations is put forward as the candidate. By a secret ballot, the Assembly then voted to accept or reject him. Had he been rejected, another candidate would have been forward. He was, in fact, unanimously accepted for the Presidency.
It should be noted that many other countries also do not have direct elections for the leader of the country. In Canada and the UK, for example, the prime ministers are elected by the national parliament. The prime ministers in these countries must already, of course, have won a seat in their respective parliaments. Likewise, the Cuban president must already have won a seat in the National Assembly.