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) 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) OR
You buy services (e.g. Google, Meta, DigitalOcean, NameCheap, Zoom, etc) outside of Estonia OR
You buy goods annually over €10 000 outside of Estonia.
If the conditions mentioned above are not met, applying for VAT-payer status is voluntary.