When you're doing genealogy on the cheap, one good place to start is the FamilySearch Research Wiki article on the locality your people lived in -- in this case, Oklahoma, United States Genealogy.
Each state article has sub-articles on Research Strategies and a guide to Online Records that are held statewide. You can also do a place-name search in the FamilySearch Catalog for United States, Oklahoma to see what is held Online, at the Family History Library, and at a Family History Center near you. Be sure to use the "places within Oklahoma" link and search all the jurisdictions at all levels (state, county, and local) where your family might have lived. The sub-article on Vital Records gives the coverage table which shows at a glance when records were kept at the local level and when they began to be held statewide.
For people who were born around 1903, you are working in the period just before statewide registration of births and deaths began in 1908 (with general compliance coming later, around 1928. But as of Monday, January 9th, 2017, researchers who have the same question about families a little later on can search the vital records indexes on the Oklahoma State Department of Health (OSDH)'s new site OK2Explore. (See New Oklahoma index site to launch, by Judy G. Russell, The Legal Genealogist, posted Jan 6, 2017.)
If you can't find statewide birth registrations, what next? Use the United States Record Selection Table or articles like Sources of Genealogical Information to get ideas of where to find the information in other records. Also keep an eye out for Delayed Birth Records (where individuals might have applied for a birth certificate later in life.
Don't neglect websites which are not immediately associated with genealogy, such as the Internet Archive. Census microfilms and other records on microfilm are being shared there, which users can browse.
For any record set you locate for free, look also for guides about how the records were created and how they are arranged. Understanding the scope of the available records is key to getting the most information out of whatever resources you have.
For more suggestions, see Determining what records are available in a particular locale?.