Heck, if is too unwieldy, as it occasionally has been, I’ve been known to use a knife and fork.
The holes are not that big & the cream cheese & lox do wonders to plug the hole but there’s no way to eat that open faced w/o getting some on your fingers.
I’ll toss in another vote for non open-faced bagel sandwiches. Mmmm, big, satisfying sandwich. I’m gonna go get one while I’m off.
All this bagel sandwichery sounds good to me, but one question: if you have a closed bagel sandwich (that is, top and bottom bagel goodness), when you bite into it won’t the squishy middle tastiness get splorted out the sides?
IME, yes, but it’s no worse than loading a burger with lettuce, tomato, pickle, onion, mustard, relish, and ketchup. That’ll splort out the sides too. You just eat it over the plate, is all; and what splorts out is on the plate, so you can use a fork to pick it up later.
Or you can do as I suggested above: just use a knife and fork from the start. Although my ex-wife wasn’t a big fan of bagels, cream cheese, and lox; she loved fully-loaded burgers, like I described above. And she pretty much always used a knife and fork to eat them.
Yes, that’s one of the problems with it. If such a bagel sandwich were consumed in a restaurant, I’d imagine even patrons at adjacent tables might be at risk of being hit with a long-distance splort! 
The big difference is that burger buns are soft. Whereas the relative hardness/stiffness of bagels is kinda like putting a splort-able squishy substance between two planks and then dropping a brick on them! 
OK, I exaggerate, but only to make the point that with bagels, open-face is generally a more manageable way to deliver sandwich ingredients. I personally don’t consider bagels a good sandwich-making bread anyway, but that’s just me. I loves me some bagels and cream cheese with coffee in the morning, but I’m not into the bagels and lox thing. When it comes to smoked or marinated salmon, I prefer to have it (open-face) on slices of baguette, optionally with wasabi and/or capers. Again, just a personal preference – I know bagels, lox, and cream cheese is a very old tradition.
That’s heresy. Do you cut up pizza, too?
Balderdash! Just use the “Thumb and Two-Finger” technique. Gently pinch your bagel half between your thumb and third finger, just below the mountain of toppings, and tuck your pinky underneath creating a bagel buttress.
If your toppings contain something splashy—say smoked whitefish salad—do a little architectural magic by plugging the hole with cream cheese and sloping it upward toward the edges. This fortress of dairy will contain those rogue drips before they turn your hand into a sticky mess.
While I approve of the usage of ‘splort’ in this thread, you may not want to look up the 3rd definition of the word in Urban Dictionary.
Absolutely. It’s much easier to keep you hands clean if you eat it open faced.
Honestly, if i were to eat that, i would deconstruct it, and eat it with a fork and knife. But i don’t like “loaded” burgers. As a kid, i refused to eat at McDonald’s because i didn’t like half the stuff they put on the sandwich.
I use my thumb and index finger around the bagel, with my middle finger underneath for support. But yes, this works fine. I rarely dirty my fingers and never actually make a mess.
Confession: i like to use a fork and knife for the first couple of bites. After the slice is small enough to be manageable i pick up the rest, and fold it NY-style to finish it.
As a concession to keeping my carbohydrate consumption down I buy bagel thins, which are the same as regular bagels but half as thick. I usually eat them with a good layer of cream cheese and a slice of lox, although I may try some of the variations toppings mentioned in this thread. I’ve never tried using them to make a sandwich, but it would solve the problem of being able to fit a bagel sandwich in one’s mouth.
Eh, if I’m eating a messy sandwich I expect to have a bit of overflow. As @Spoons said, just eat it over the plate, and when you’re done? Huzzah! There’s “leftovers” on the plate to extend your eating pleasure. 
Nothing disappoints me more than an underfilled sandwich with just bread and a small amount of filling. I like sandwiches with a lot of stuff in them. Like a Banh Mi. Yum!
There is something between this and the stuffed-to-overflowing Dagwood. Just sayin’. 
Oh, sure, but I’m a more is better than less kinda person.
I like sandwiches that don’t have too much bread. I can have a second if I’m still hungry. But overfilling a sandwich that already has too much bread doesn’t solve the problem, imho.
I live by “nothing succeeds like excess” myself.
Or to put my opinion another way, i follow in the style of the Earl of Sandwich, who wanted to be able to eat lunch without taking a break from his card game or soiling his cards. If a sandwich doesn’t fulfill the purpose of being easy to eat with just my hands, then i see no reason to assemble the ingredients into a messy pile, and I’d just as soon eat them with a fork and knife on a plate.
Why no, i don’t eat a ton of sandwiches. But i do like a nice open faced bagel sandwich. And sometimes a tuna salad sandwich or a pb&j hits the spot, or will be easy to pack for lunch.
Maybe I have issues with open-faced sandwiches because I always seem to get some on my nose. I don’t think my nose is that big!
It’s probably your angle of approach.
Another vote here for open-faced with bagels, much less splorting.
When you eat a bag with toppings open-face, you taste the toppings more because they go directly to your taste buds.
And letting the insides squish out onto the plate defeats the whole point of having a sandwich. May as well just have a Sloppy Joe.