The meal where this sacrament was instituted is commonly called the Last Supper. It is called last because it was the last meal that Jesus ate before His arrest, and of course this attribution makes sense at that level.
But there is also a real sense in which we ought to think of it as the First Supper. This was the meal where Christ instituted this memorial. It was the first observance of countless millions of observances. The Passover that Moses had the people celebrate was their last meal in Egypt, but it was the first Passover. The meal that Jesus established was His last meal before His death, but it was also the last true meal of the old creation.
Of course, both first and last remain fitting terms for it. Christ is Himself the First and the Last, and this is the foundational meal (first) and the ultimate, eschatological meal (last). Christ is everything to us—He is the cornerstone, and He is the capstone. He is the one who strengthens us for our journey and pilgrimage the day we begin it, and He is the one welcoming us home when we arrive there. He is the one in whom we live and move and have our being.
So not only does He commission and send us, and then welcome and receive us, so also He is present with us every step of the way, accompanying us through His Spirit. We affirm the real presence of Christ here because the Spirit of Christ indwells every faithful believer who partakes of this meal in faith.
The Lord offers Himself in the gospel and in the bread and wine, and the Lord, dwelling in us by His Spirit, receives what is offered by stirring up true faith within us. He offers Himself, He is what is offered, and He receives what is offered, equipping us as He does so. He does this through the instrumentality of living faith, which lives and abides in you.
So come, and welcome, to Jesus Christ.