The question refers to Section 136 of the Equality Act 2010. The Equality Act unified several different previous legal regimes relating to various kinds of discrimination - on the basis of sex, race, disability, etc. A common feature of those regimes, although not expressed in exactly the same way in each case, was the manner of convincing a court that discrimination had taken place. Section 136 carries forward the essential nature of what was done previously, but in a more uniform manner (for example, this now applies to disability discrimination in general, not just in the context of employment, unlike in the Disability Discrimination Act 1995).
The idea of shifting the burden of proof is expressed as follows in the statute (subsection 6, omitted, is merely technical, listing several tribunals which are to be treated as courts):
(1) This section applies to any proceedings relating to a contravention of this Act.
(2) If there are facts from which the court could decide, in the absence of any other explanation, that a person (A) contravened the provision concerned, the court must hold that the contravention occurred.
(3) But subsection (2) does not apply if A shows that A did not contravene the provision.
(4) The reference to a contravention of this Act includes a reference to a breach of an equality clause or rule.
(5) This section does not apply to proceedings for an offence under this Act.
This is what is going on with the question's reference to "making out the preliminary facts", i.e. evidence submitted by the claimant for the purposes of subsection (2).
The standard of proof is the normal civil standard: the balance of probabilities. That is because by subsection (5), the provisions only apply to civil claims and not criminal prosecutions.
The language of the section might suggest that there is a sort of two-phase process here, but the actual procedure of receiving evidence does not have to follow that structure. The court/tribunal can take in submissions from both parties, and then apply an analysis once everything has been presented. See Royal Mail v Efobi  UKSC 33, Lord Leggatt at paragraph 30:
[I]t follows from the application of this basic rule of evidence that an employment tribunal may only find that “there are facts” for the purpose of section 136(2) of the 2010 Act if the tribunal concludes that it is more likely than not that the relevant assertions are true. This means that the claimant has the burden of proving, on the balance of probabilities, those matters which he or she wishes the tribunal to find as facts from which the inference could properly be drawn (in the absence of any other explanation) that an unlawful act was committed. This is not the whole picture since, as discussed, along with those facts which the claimant proves, the tribunal must also take account of any facts proved by the respondent which would prevent the necessary inference from being drawn. But that does not alter the position that, under section 136(2) of the 2010 Act just as under the old provisions, the initial burden of proof is on the claimant to prove facts which are sufficient to shift the burden of proof to the respondent.
It follows that the nature of the evidence submitted does matter, especially regarding anything that the respondent will be likely to dispute. If the claimant is fortunate and the respondent does not respond at all, then they may get a default judgment. Or a decision might be reached at an early stage that the claimant has simply failed to establish that unfair treatment has occurred at all. Or it might take an extensive series of hearings with cross-examination of witnesses.