Maybe, maybe not. While working at this large corporation did you develop work patterns and skills that are currently favored? (Agile being the code word most use) Are you conversant in the aspects of the stack that your employers are looking for?
So here is the thing, if you haven't, then you're coming in as basically a much more junior person than you might think. You are going to have to learn the new stack or the new skills, and as with any hire, there wouldn't be an existing track record to show how well you might do at it.
Here is the second thing, you're self labeling as a software architect / tech lead. One of the things that I have seen is that the idea of architect and tech lead varies quite a bit from company to company. If you're characterization of what your role is, is one that doesn't exist in the company where you are interviewing, then you're being slotted into the "we have to retrain this guy for one of our roles."
And the final thing, if your title is affecting your perception of your contribution, especially at a smaller company, then you've got to work through that. The only use for titles in a company of fewer 50 people is so that customers and partners can get a sense of your decision level. For you personally, your role has to come from inside yourself. If that is the kind of person you are, then you will be that kind of person in your new job and people will know you for it. What they call you in the offer letter is often irrelevant. In the Bay Area at least that is typically code for a salary range.
Don't get hung up on the title. Talk to the hiring manager about the kinds of things you would expect to be doing at the company and the ways you would expect to contribute. They will pick a title that reflects that.