Yep, if you're riding like that you should already be in the big ring. Specially if you are that close to being in your smallest rear cog.
Modern bikes with pinned and ramped chainrings are usually very reliable shifting. Old style flat rings sometimes would rattle a bit before shifting under load.
But a front shift will always be a bit slower. Check your limit screw isn't set too tight and you don't have too much slack in your shift cable. Front derailleur adjustment is an art and small tweaks are not unusual to get perfect shifting.