If I get there the day after the crime, it's a banner day.
Usually, private investigator get to the scene of the crime somewhere between several months to several years after the event in question happened. There's usually no sign of the alleged crime. There's usually not even residual crime scene tape.
So, why would a private investigator spend too much time worrying about crime scene analysis? Couple of reasons and a couple of approaches.
Reason 1 - It's helpful to understand how the police procedurally analyze a crime scene. This lets the private investigator understand crime scene photos, scales, evidence markers and other nuances of the process. These are good to know, from a conceptual perspective.
Reason 2 - On a deeper, more granular level, if the investigator knows procedure an protocol from the police, the investigator can spot deficiencies - places where the police didn't follow protocol, or side-stepped procedure. These are great things to know. That said, there is no need for a private investigator to be a crime scene expert. A working knowledge will do just fine.
Approach 1 - Some private investigators specialize in crime scene analysis. That's cool. If that's your gig, do it and do it well. Most of us, however, are not experts. Can't be. We have more work to do that typically has more of a bearing on how our case works out than analyzing crime scenes. I'm thinking of witness interviews, document reviews, etc. If you're a crime scene expert, you should probably focus on that and that alone. If you're a crime scene expert, and a voice stress analysis expert, and a ballistics expert, and a cell tower expert, and a micro-expression expert, and a polygraph expert, and a latent fingerprint expert ... If you're an expert in all of these fields, then there's a good chance you're not an expert at all. You're more likely a person who chases certifications. It's neigh impossible to be an actual expert in so many disparate fields.
Approach 2 - Understand the basics. Review the procedures and protocols, make sure the bases were covered. Then move on to interviewing witnesses and checking/verifying stories. Witness says they saw the whole thing from across the street, check the sight lines. Witness says they identified the suspect from around the corner, check the sight lines. Check them at night (same time the witness claims). Check, verify, confirm.
If there's a need for an expert crime scene analyst, you can look like a hero by referring your lawyer client to an actual expert, someone who has spent a career doing that one thing.