It will depend on the client's risk appetite and budget.
Most construction projects progress through various discrete phases from customer needs analysis to financing to site selection to due diligence checks to supply chain contracts to construction build to quality control to safety management to customer sign off to snagging etc etc etc and with lots of iteration throughout (not simply linear as described here).
Therefore if the client wishes to avoid risk and has sufficient budget to do so, risk identification should, ideally, be continuous throughout the phases of construction.
Otherwise, risks could emerge which were not anticipated resulting in unnecessary crises.
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You could apply , before, and during the construction project, PERT, Program Evaluation and Review Technique , a well known, and old tool, that can be found in many books about Operations Research, in order to localize the bottlenecks. And, by the way, "the best time" does not exist: you have to define the possible objectives, there are almost always competing objectives, so , then you have to find a defendable trade-off. And further I would suggest to constantly monitor a construction project, and to keep talking with those, who are involved in the construction project. Always cooperate, talk, monitor, and do not stick to a top-down-approach!
Risks could be project specific, environmental or politics related amongst others factors. A formidable risk identification should start from project initiation(inception) through planning and construction stages.
PMI recommends Risk Identifications as early as in a project . This will help the PM to plan for the risk and prepare your strategies against identified risks.
Risk Identification should not be a One time activity and to be performed at frequent intervals through out the project life cycle . A risk can evolve right at the beginning of project or at the minute before closing a project . Risk Management is a iterative activity .
Identify your Stakeholders and Risk and address as early as possible . That's one of key for success in project management.