If IRS does a random audit, will they ask for a birth certificate and Social Security card of your dependents, or does that mean they suspect something?
In order to claim a child as a dependent, your child must have a social security number (or ITIN) before the due date of your return, and the name you use on the form needs to match the name on the Social Security card. (See Form 1040 Instructions.)
If you get a random audit, in which they go over your entire return, I think it is possible that they would want to see the card. Keep in mind that the IRS can look up Social Security numbers; they would probably only ask to see your card if there was an issue where they couldn’t verify the number you entered on the return. If you simply lost it, you can contact the Social Security Administration and get a replacement. But if you don’t have a number for your child, you will need to apply for a number before you file your taxes.
Read this page from the IRS to learn more about the audit process.
IRS audits are rarely random; they usually have specific cause to believe that something is incorrect, which could include something as simple as a mistake in entering your child's Social Security Number on your tax return this year. There is a type of audit (called a Taxpayer Compliance Measurement Program (TCMP) audit) where the IRS chooses a return at random and asks the taxpayer to provide proof of every entry on the tax return, including a marriage certificate if you claim to be married, and birth certificates and Social Security Numbers for dependent children, and similar information for other dependents if any etc. As Ben Miller's answer notes, if you (or your child) have lost or cannot find the Social Security Card, you can contact the Social Security Administration for a replacement.
A TCMP audit does not mean that the IRS suspects something; it merely means that the luck of the draw has selected you to be one of the samples that the IRS is using to measure how well people in general are complying with the IRS rules and regulations, and filling out the forms correctly. The IRS will draw various conclusions about how well people are doing in complying with the law (and also about how clear the IRS instructions are and whether ambiguous instructions are complicating the problems) from those returns that are selected for the TCMP audit.