"Boeing had had its claws into the space industry since the dawn of spaceflight," - Muilenburg claim
Pardon me while I splutter. Actual practical space flight dawned with - well, it's hard to pin-point exactly, but von Braun's A4 (V2) rocket has some claim to being the first practical rocket able to reach space. Apparently an A4 was the first man-made object to pass the Kármán line, in 1944. Boeing wasn't involved.
Nor was Boeing involved when the USA stuck a WAC Corporal sounding rocket on top of an A4/V2 to reach far higher altitudes in 1948-1050. The WAC Corporal was a joint Douglas/Guggenheim Aeronautical lab project. The Redstone rocket, which formed the first stage of the USA's first successful satellite launcher, was made by Chrysler. The Sergeant rockets making up its second and third stages were designed by the JPL and made by Sperry.
All this happened after the USSR had launched Sputnik - again without any Boeing involvement.
Other notable early US entries in the space flight ledger include missiles such as the Atlas, later adapted into satellite launch vehicles - built by Convair (part of General Dynamics).
Boeing did end up with the Delta rocket under its wing on account of buying McDonnell-Douglas. The Delta rocket was a Douglas project originally derived from the Thor missile by Douglas (airframe and integration), Rocketdyne (part of NAA), AC Spark Plug (inertial guidance), Bell Labs (radio guidance), and GE (re-entry vehicle).
Perhaps one could argue Boeing was involved right from the earliest days of space flight because Boeing has since bought a lot of the firms that were actually involved at the time, but that seems to be about it.