Yes, they used blueprints in at least some cases. The Roman Vitruvius writes about how knowledge of geometry helps the architect use straight-edges and compasses in making plans for buildings. He also writes about other drawings of use to the architect besides blueprints. He talks about such plans quite a bit in his work and puts a lot of emphasis on how important they are.

Arrangement includes the putting of things in their proper places and the elegance of effect which is due to adjustments appropriate to the character of the work. Its forms of expression (Greek ἱδἑαι) are these: groundplan, elevation, and perspective. A groundplan is made by the proper successive use of compasses and rule, through which we get outlines for the plane surfaces of buildings. An elevation is a picture of the front of a building, set upright and properly drawn in the proportions of the contemplated work. Perspective is the method of sketching a front with the sides withdrawing into the background, the lines all meeting in the centre of a circle.

Vitruvius, On Architecture, II.2

There are a few surviving plans, but it is a bit unclear if they were actually used by architects or builders or were instead maps of existing areas or simply doodles. Some were etched in stone and others were on papyrus. One was made into a mosaic, which might be interesting to look at but would have been immobile and probably useless to an architect on a building site.

One funerary plaque in Perugia appears to include a direct transcription of architectural plans. It consists of three separate plans which are all in different scales, which leads scholars to believe they represent three different blueprints which were put next to each other on the plaque. You can see it here: https://upload.wikimedia.org/wikipedia/commons/5/52/IMG_1082_-Perugia-Museo_archeologico-Mappa_romana-7_ago_2006-_Foto_G._Dall'Orto.jpg

We also have some surviving models which were probably used during the building process. It has been guessed that these models may have been used as blueprints or in conjunction with them. One is a 1:24 scale model of a temple in Lebanon. Another is a 1:30 model of the Great Altar of Baalbek.

In Egypt there is a papyrus which shows the elevation of the shrine and has been dated to the eighteenth dynasty. This is a bit younger than the pyramids.

Sources: Vitruvius and Rubun Taylor, Roman Builders: A Study in Architectural Process