USS Saratoga was hull number CV-3. USS Lexington was CV-2, but was commissioned after Saratoga (both in 1927, though Sara was launched in 1925). However, as the hull numbers suggest, there was a CV-1, USS Langley, recommissioned as a carrier in 1922.
Langley was a converted collier. By WW2 she had been deemed unsuitable for fleet carrier operation and converted to a seaplane tender. Like Langley, Lex and Sara were also conversions, done during construction. Both were designed to be battle cruisers, but the 1922 Washington Naval Treaty forbade building battleships and battle cruisers. The first purpose-built USN carrier was USS Ranger, CV-4. Ranger's limitations led to her not being used in PTO combat operations in WW2. The Yorktown and Essex class CVs were quite successful, as were the Independence class CVLs (converted from cruisers during construction).
I'm not suggesting carriers will forever be viable, just that the last 40+ years justify skepticism of, "Carriers are doomed!" claims.