For the HiLumi LHC Upgrade (HL-LHC), new high field and large-aperture quadrupole magnets for the low-beta inner triplets (Q1, Q2, Q3) are being built. These new quadrupole magnets are based on Nb3Sn superconducting technology. As part of the US-HiLumi Accelerator Upgrade Project (AUP), ten Cryostat Assemblies (LQXFA) for Q1 and Q3 replacement will be built, tested, and delivered to CERN. The first LQXFA was assembled and tested at Fermi National Accelerator Laboratory (FNAL) during fall 2022 and spring/summer 2023, respectively. This paper summarizes the assembly process and experience of the first LQXFA Cryostat Assembly at FNAL.