You can, in contrast, say a "p" in isolation, as it is the unvoiced consonant. But the English "p" is actually two sounds-- there's the lips-puffing-air sound, and the lips-stopping-air sound. The same letter is used for both, because context allows them to be coded correctly (subject to accents). Usually, the puff is at the start of a syllable, and either one can be at the end. This is one case where the teacher might not be able to distinguish the two sounds, but the student might be able to recognize them as different, because they don't already have the association that they are both represented by the same letter in English.
"B" is the voiced equivalent, but as voicing comes from the larynx and not the lips, you need an additional symbol to characterize that part of the sound. In that sense, "b" is the combining symbol for "p" and an adjacent voiced sound.
This is why Greek codes English "b" sounds as "μπ". Their "β" is more like partway between "v" and "b" than an English "b". Doing this language hack leaves a mark, so if your name starts with a hard "b", you might be able to detect a native Greek speaker still voicing an "m" before your name, or mispronouncing a "b" in your name as an almost v-like beta. I'd be "Log from Mblammo", for instance, and you might be "Mburfog". If someone teaches the phonics incorrectly, it might leave a similar residue in the student's speech.
Since "b" is not an atomic mouth sound, I wouldn't teach it before "p". I'd introduce it with other voice-added sounds, and use whispering and yelling (for some reason, my kids thought it was fun to yell) or normally-voiced speech to help tell the difference. Like when you whisper "cup" and "cub", they sound the same, but when you yell them, they are different. The "p" stops the voicing at the letter boundary; the "b" lets it bleed through from either side. That's why the "b" can't be by itself--a lone "b" is just a whispered "b", which is actually a "p".
Practice voicing boundaries with "pop", "bop", "pub", "bub", "tot", "dot", "tad", "dad", etc. It might also help reinforce that the written symbols are encoded speech sounds, and that means they have to describe what the lips, tongue, cheeks, jaw, and larynx are doing.
And you might as well tell the student that accents happen when some of the encoding rules get changed. Play a video of someone with a tough-to-understand accent speaking, have the student read a transcript, and then watch it again. One that immediately leaps to mind as kid-friendly is Merida in "Wreck-It-Ralph 2", who essentially says, "May your hearth stay warm, and your pantry full. Come back soon.", but no one else can understand the dialect. Somewhat less kid-friendly is the scene in "Hot Fuzz" that translates a very Northern accent in multiple progressively less-Northern stages, until it can be understood by someone from London.