• Calvin Coolidge was sworn-in by his father, a notary public, in the early morning hours of August 3, 1923. He delivered his first State of the Union four months later on December 6.
• Harry Truman was sworn-in on April 12, 1945. Although he addressed a joint session of Congress four days later on the prosecution of the war, he didn't deliver his first proper State of the Union until January 6, 1947. (He did, however, address two additional joint-sessions of Congress in October, 1945 and May, 1946.)
• Lyndon Johnson was sworn-in on November 22, 1963. He delivered his first State of the Union on January 8, 1964.
• Gerald Ford was sworn-in on August 9, 1974. He addressed joint-sessions of Congress on August 12 and October 8, before delivering his first State of the Union on January 15, 1975.

Source: Office of the Clerk of the House of Representatives

TL;DR: Presidents give State of the Union addresses whenever they feel like it. The State of the Union is usually, but not always, the very first address a new President gives to both houses of Congress.

When a new President must address Congress for reasons of unusual circumstances, or because of the date, the speech given is typically called [President's] First Address to a Joint Session of Congress or not even given a name at all, while still essentially being a State of the Union address.

President Obama's first SOTU address was simply called an Address to a Joint Session of Congress, as was President Trump's.

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Long backstory: The First State of the Union address was given on January 8, 1790, almost a year after President Washington's inauguration on March 4/April 30, 1789. This speech detailed the events that had occurred in 1789, such as the admission of North Carolina to the Union, and laid out (in very broad terms) Washington's agenda.

Washington would continue to give seven more addresses until December 7, 1796 before his successor, John Adams took office on March 4, 1797.

Now, the early State of the Union addresses were typically given sometime during the Winter, (During Washington's first term they were seemingly delivered whenever he felt like addressing Congress) and were usually the first addresses a new President gave to both houses of Congress.

Adams was the first President elected after Washington, and was a member of the Federalist political party, who Washington tended to ally with regarding policy. The first speech Adams gave before Congress came only 5 months after Washington's last SOTU, and only 2 months after Adams' inauguration.

Giving a State of the Union address this early into Adams' presidency would have been odd to say the least, but there were still important matters that needed addressing. The Quasi-War with France loomed over the United States, and the President felt it was necessary to address Congress.

In giving to Congress information of the state of the Union and recommending to their consideration such measures as appear to me to be necessary or expedient, according to my constitutional duty, the causes and the objects of the present extraordinary session will be explained.

Even though this was President Adams' first speech to Congress during his Presidency, it's not considered his First State of the Union address, even though he somewhat ironically used the phrase "state of the Union" in this address, and not in what we consider to believe his first official State of the Union address. Overall, President Adams gave five addresses to a joint session of Congress, but only four of those are counted as official State of the Union addresses. Fortunately, Thomas Jefferson resolved this confusing mess by eliminating the spoken State of the Union address entirely.

After Jefferson stopped addressing Congress in person, the number of Joint Sessions held by Congress decreased dramatically from what it had been during the Federalists' years.

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^When ^I ^say ^given ^or ^delivered ^or ^something ^during ^the ^following ^examples, ^I ^mean ^that ^the ^President ^in ^question ^gave ^a ^letter ^to ^Congress, ^who ^then ^read ^it ^out ^loud.

William Henry Harrison and the Curse of Tippecanoe

Our 9th President, William Henry Harrison was the first President to die in office, and one of two Presidents to have never given a State of the Union address to Congress.

John Tyler gave the 1841 State of the Union address to Congress 8 months after the death of President Harrison.

Zachary Taylor's Bad Luck

On December 4, 1849, Zachary Taylor's first and only State of the Union address was delivered to Congress.

He would die seven months later, with President Millard Filmore giving the 1850 State of the Union to Congress on December 2nd.

Abraham Lincoln

After being reelected, President Lincoln died 1 month into his second term, leaving Andrew Johnson to give four full State of the Union Addresses.

James A. Garfield

Much like Old Tippecanoe up there, President Garfield is the second and final President to have never given a State of the Union address to Congress. Garfield died on September 19, 1881, six months after his inauguration.

Chester A. Arthur would give the 1881 State of the Union to Congress on December 6th.

William McKinley

Much like Lincoln, McKinley died 6 months into his second term on September 14, 1901, leaving Theodore Roosevelt to give four full State of the Union addresses beginning 3 months later on December 3 1901, and would later give four more during his second/first elected term as President.

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^After ^Wilson ^took ^office, ^the ^State ^of ^the ^Union ^was ^delivered ^in ^person ^again. ^When ^I ^say ^given ^or ^delivered ^here, ^I ^really ^mean ^the ^President ^spoke ^in ^front ^of ^Congress.

Woodrow Wilson's Word Wars

Woodrow Wilson was tremendously proud of his oratory skills, and revived the tradition of speaking before Congress by delivering three addresses before his first official State of the Union on December 2, 1913. In totality, President Wilson would speak before Congress a whopping 23 times.

Warren G. Harding

President Harding managed to beat President Taylor by one speech, giving two State of the Union addresses to Congress before his death, 2 years into his first term on August 2, 1923. Despite this, he delivered seven addresses to Congress before his demise.

Calvin Coolidge would go on to give the final two State of the Union addresses of Harding's term beginning 4 months later on December 6, 1923, before giving four more in his own right as President.

Franklin D. Roosevelt

Despite being the longest serving President in history, FDR gave fewer speeches than Wilson did, giving twelve State of the Union addresses before dying 2 months into his fourth term on April 12th, 1945.

Harry S. Truman would go on to deliver the final three State of the Union addresses of FDR's fourth term beginning January 21, 1946 as well as many other addresses, before giving five State of the Union addresses in his own right.

Just before Roosevelt's first term, the twentieth amendment was passed, changing Inauguration Day from March 4th to January 20th. Roosevelt's fourth term began on January 20, 1945, while Truman would be inaugurated on April 12th, the same day Roosevelt died.

Truman spoke before Congress shortly after Roosevelt's death on April 16, 1945 and gave many subsequent speeches before his first official State of the Union address on January 21st, 1946.

John F. Kennedy

Kennedy delivered only three State of the Union addresses before dying 2 years into his first term on November 22, 1963.

Lyndon B. Johnson would go on to give the final State of the Union address of Kennedy's term on January 8, 1964, before giving five more in his own right.

Richard Nixon

Richard Nixon gave five State of the Union addresses before resigning 1 year into his second term on August 12, 1974.

Gerald Ford would go on to give the final three State of the Union addresses of Nixon's second term beginning on January 15, 1975, but spoke to Congress once before on October 8, 1974.