Samuel Armstrong began playing the trombone at the age of 12 and his primary teachers were Byron Peebles and James Miller of the Los Angeles Philharmonic. In 2007, he won first prize at the Pasadena Showcase Competition and was a finalist at the International Trombone Association "Gagliardi" Competition. He was also a featured soloist at the MidEurope Festival in Schladming, Austria. Samuel later became principal trombone of the prestigious American Youth Symphony, performing with Hollywood greats Alan Silvestri, David Newman and John Williams. 

In 2008, Samuel began his studies with Joseph Alessi at The Juilliard School, receiving the Jerome L. Greene Fellowship.

While in New York, he had the opportunity to collaborate with composers John Adams, John Corigliano, and Steve Reich as well as record works by John Zorn and Jonathan Dawe. In 2013, Samuel premiered Erhu Suite by Los Angeles based film composer Nathan Wang (adapted for wind ensemble by Charles Fernandez). Erhu Suite consisted of themes originally scored for a 72 episode Chinese television series about the life of general Yue Fei. Later, Samuel toured with the L.A. Symphonic Winds throughout China performing this work with his brother, Michael Armstrong, at the podium. These concerts were met with acclaim in cities including Hangzhou, Nanchang, Ningbo, Shanghai and Taicang.

In 2015, Samuel graduated from the Curtis Institute of Music, receiving the Ruth and Morris Williams Jr. Scholarship while studying with Nitzan Haroz and Matthew Vaughn. 

Prior to joining the Singapore Symphony Orchestra, Samuel was appointed Co-Principal of the Malaysian Philharmonic Orchestra and has performed with the Los Angeles Philharmonic.