First of all, I'd like to direct you to one of my better answers. What it'll teach you is that, fundamentally, it's already very difficult to reverse engineer almost anything. Not impossible, but not easy.
Add to what that other answer explains the fact that you don't have an integrated circuit or a piece of encrypted software. You have the result of the application of the technology someone is trying to reverse engineer. Let me explain.
Reverse engineering an integrated circuit means re-creating the schematic diagram. But not re-creating the fabrication facility. There's never an assumption of an overwhelming leap in innovation (real innovation doesn't work that way, no matter what the magazines claim). In other words, while one might need to tweak how a fabrication facility works, it's always possible to re-create the chip. Said another way, a lot of assumptions can be made based on "we know how to do X and they appear to do Y," and since chip manufacturing is kinda all the same thing, it can be assumed that F(x) = y, which gets you further than you might think.
But unlike an integrated circuit (and making allowances for talking about a non-existent, even fanciful technology) there's really nothing about a genetically engineered creature that explains how that creature came to exist. There isn't, so to speak, a cross-section of the silicon substrate that can be examined to reveal information about the fabrication facility. It's a vague area within which you can achieve your goal. I have before me a completely new kind of frog! I know how to clone frogs! But that doesn't mean I can know, only through examination, how to build the equipment that produced that new frog.
And that's a wordy way of explaining why your tech can't be reverse engineered (at least not quickly... I'll get to that in a moment). We can look at the loaf of bread, but that doesn't mean we know anything about yeast, how to create it, or how to use it... or ovens... or rolling pins.... Whatever device was used to create our biologic, it's that device that needs to be reverse engineered. It's like trying to reverse engineer a chip fabrication facility when all you have to work with is an example chip. Yeah. You're well within the world of suspension of disbelief.
Now, having said that, there is a caveat. In that other answer, the OP was asking about an object the physics of which we did not understand and the operation of which we did not understand. (There were problems with that OP's assumptions, read the answer to understand that.) But it's an important distinction. You see...
Anything invented by one human can be invented by another.
In fact, the history of science is replete with examples of multiple scientists/engineers/inventors coming up with a solution to the same problem at about the same time despite acting independently. Unless you're proposing the innovative leap in your world isn't just a leap, but a world-record setting power jump way, way, way beyond a reasonable "realistic" expectation, what you have is the discovery of a technology that need only wait for someone else to discover it.
In short, while reverse engineering is whomping difficult, it's not impossible unless you're introducing Clarkean magic, as the other OP did.
So, while it's believable that people can't reverse engineer your biotech because extrapolating the devices needed to create a biolgic is not (at all) a direct and reasonable conclusion based only on looking at a genetically engineered sample, the reality is that there's a window of time before the first sample capture and the day that everybody has the tech.
You get to set the size of that period of time. Saying "it can't be done" is simply deciding the period of time is outside the window of your story.