Start here: what does your own health system provide?
Before any conversation about private cost, confirm what your own health system already provides, because correction of a congenital difference affecting function or carrying a health risk is treated as core paediatric care in most developed systems, usually at no direct cost to the family.
In the UK, this is delivered through paediatric plastic surgery and hand surgery services as part of the NHS, with access to the wider team, therapy, orthopaedic input and genetic assessment that the pathway depends on. In many other countries, correction of congenital differences is either mandated to be covered by health insurers or is a standard part of funded paediatric care. This varies by country and by the specific condition, which is why confirming your child’s particular entitlement, through the paediatric team already involved or your own health system directly, is the genuinely important first step rather than an afterthought.
Where funding is confirmed, staying within that system for the whole pathway, rather than arranging surgery separately abroad, is generally the path that keeps the therapy, review and later-stage planning joined up, which matters more in this category than almost any other on this site.