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My Bosch micro/oven need 120 volt 20 Amp receptacle. I do not have a 20 Amp circuit breaker for this purpose. Can I couple two separate 15 Amp breakers as a dedicated source to provide higher Amperage limit (20 Amp)? Theoretically this will increase wire cross-section area for a higher Amp. limit. Is it permissible by code?

Paralleling is NOT Allowed

You can't do this (except under very limited circumstances that don't apply to your situation). The problem (ignoring the code violation) is that if one of those wires breaks (disconnected at any point between device and breaker) then all of the current will flow on one wire, which is not safe as it would put all 20A on one wire.

You also must NOT simply replace the 15A breaker with a 20A breaker. Almost definitely the existing wire is 14 AWG, rated for 15A, and not 12 AWG (or larger) rated for 20A. So upsizing the breaker without upsizing the wire will also be a real fire hazard (and code violation).

The only real solution is to replace the wire and the breaker (i.e., a new circuit) or to find an oven that is rated to run on a 15A circuit.

Absolutely not!

Circuit breakers don’t work like that.
Did your microwave come with a plug that has 1 straight blade and 1 blade at 90 degrees? If so you will probably need a dedicated 20 amp circuit with #12 wire.
2 breakers depending on how located in the panel could provide 240v and if connected together “boom”
If they could be paralleled they would not work correctly as breakers are inverse time devices.
And as mentioned above if you have 15 amp breakers your wiring is probably only 14 gauge and 15 amp is the max breaker size. Large micro waves are one of the few devices that I have seen that require a 20 amp circuit so if the blades are not parallel 15 amp you will need a new circuit.
To parallel wires they have to be 1/0 or larger, we do not parallel breakers.

The short answer is NO. Of course it might help to explain why.

"In theory" this would work as you expect (the part about increasing the wire cross section), but it's forbidden by code because there are a lot of dangerous issues related to this as well as practical ones.

You can't use two 15 amp breakers because that would still trip at 15 amps. You might be tempted to take two existing 15A circuits and connect them both to a 20A breaker, and that would "double" your wire size and work, but it's not safe. If there is just one bad connection somewhere (or a connection goes bad over time), the circuit would appear to work fine, but you would be pulling all that current over one wire instead of two which would overheat and potentially cause a fire. Even with all of that there's still the problem of trying to connect those two wires to devices that only expect one larger wire.

Nope. You are not allowed to parallel conductors like that.