I don't think that an antigen designs the antibody, per se. Diversity in antibody repertoire is the result of rearrangements in VDJ or VJ chain genes apart from somatic hypermutation and affinity maturation. Although on an evolutionary timescale the repertoire is shaped by factors like environments, population structure, microbial load etc. The body mostly has antibodies already against the hitherto unforeseen antigen, all it needs to do is clonally expand the populations of antigen-specific IgM response followed by IgG dominated immune response.

I hope that I understand your question correctly. As Vipul Batra mentioned already, antigen-selective IgM is considered to be this "biomarker," and it is used exactly for this purpose.

Vipul Batra Michael G. Weller if I'm understanding correctly, there is such wide diversity of antibodies that we have one for almost any potential antigen, it's just a matter of cloning these, correct? Then I'm confused what the role of IgM is. It seems counterintuitive that one antibody, IgM, could be antigen-specific... let me know if I'm misunderstanding something!

The immune system is extremely complex. https://en.m.wikipedia.org/wiki/Immune_system might be a good start. To answer you question briefly: There are billions of different IgM potentially against all kinds of antigens. They are produced at the first contact. After some time, the IgM production is stopped and IgG-type antibodies are produced.

Michael G. Weller ah, IgM and IgG are types of antibodies, not individual ones?

Yes, these types are called classes: https://en.m.wikipedia.org/wiki/Antibody#Classes

Michael G. Weller got it, that was my confusion. Thank you for clarifying, Mr. Weller