You can start selling your service(s) without a VAT number, but it's obligatory to register your company as a VAT payer if:
Your turnover reaches €40 000, from the beginning of a calendar year (an exception applies when selling EXCLUSIVELY outside the EU) AND/OR
You start providing 'digital' services (software, digital content etc) to individuals or companies in the European Union without a valid VAT number based on VIES database (meaning that your company has to be registered for the OSS Scheme)
If neither of the conditions mentioned above are met, applying for VAT-payer status is voluntary.
When deciding whether to register your company as a VAT payer or not, you should also consider your expenses, as the location of your potential customers and suppliers impacts the result from a VAT perspective.